MCQ Bank
Which of the following discretized factor is utilized to check the stability of finite difference scheme in Fourier transform,
- A) data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJIAAAAsCAIAAAAB2XbcAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAOASURBVHhe7ZhhseowEIWxgAYs4AEJaMACDnCAAxSgAAMYwAEe+r7h7O3stJCmj/TeBvb7wXRDmiZ7sieFRRNUSMhWJSFblYRsVRKyVUnIViUhW5WEbFUSslVJyFYlIVuVhGxV8qWyHQ6H5XJpQR6bzWbx4Hw+E55OJ4W3200dfpMvlQ0NwII87vc7Iu33e4ubhuux2pciTDKX6/WKbJfLxeKm2e122+3Wgt/l62Qj7w9vWyCDNeVxPB65y4IHq9UKs+WCT40pUXFRqpBvKVBCirL9qhQfJRtpIoPr9VpJJHdUQ//sUZYtyIahvK8yLINIDHYAz2JY6UQVckEL5x+a8UlL2SPwc2Qjd2xwNFMqSRxZJrNKpYdUjj3YQMJY8CgpBkcMadNXBamYDDVqcVE+RDbtbtLkRSKztFjgoJFEW5CHry0h6xNP/RaNmZIFpfkQ2XAw0pdzfqArPfUSn49e9/2eQHsequ3S3wQIqVov640tKdm0X8DvJu2yiWbzf6gUMn2vNTeLHSwTZ2O9dMBv/aqlgQU/2qMl17qFFjLDJz2lGdd6Z2EzqWdBXsqGKfMwHsn8vKezy5iNBYVQUtIkKkk7KTM1dH46f9UTKyXdgBLtPqDxMYUFCqnFa49IdGZMzZD21qt1YztOQQZMUrL5jPjZzwTSxKyUqUHo3J8/qWcEvztR4q9+k+UwIJv2S2spfRVBjYlqYBCyYMEE8HTEsODHM0Vnp6uk+lNFIc0Q7akk7iL0Jjk3BmRjAd5Snh5s/d+hHRgELCiNNk1nfJkYM29LUN1oeeqlfCVQi6FYUWbt/hUDsrESbykse4q6IVPKWoJX1ZyQzZteAo2Q2XkmpGTrrAf9kK3j+KiYWLNGgEkNh/G9SYJc4ZXSHfqyMVtGsGCWDMumBbAq7AWREA+T1E8W2nWQJBLEjXSwYBokkv6PYFYy7VEPZTu2r38sk3DOBxsMrE32xTKwHUIliMZ2VZJW10/hlo6DTQGbg0lqqlzDqPdAlqPXUeDGzuE9Q96tg0FVSIfqNSjIu7KlVcF22L+q1KAg78qGKhwGghB38m8HeqObv+dUR4FqQ5i24JCN00XXQLsPg1K8K1sH3jNRzoIX/yQF71NSNszQi4RtUoiZP56CURSuNqFfBdijDrygOJPIFkxNyFYlIVuVhGxVErJVSchWJSFblYRsFdI0/wDVDvrE5xxAHgAAAABJRU5ErkJggg==.
- B) data:image/png;base64,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.
- C) data:image/png;base64,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.
- D) data:image/png;base64,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.
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- B) data:image/png;base64,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 .
- C) data:image/png;base64,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 .
- D) data:image/png;base64,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 .
The Fourier method for stability analysis of PDEs is mainly used to:
- A) Solve the PDE analytically
- B) Optimize the grid spacing
- C) Approximate boundary conditions
- D) Determine whether numerical errors grow, decay, or remain bounded over time
In Jacobi’s method for a 2D Laplace equation on a uniform grid, the value at an interior point (i, j) is updated using:
- A) The average of its four nearest neighbors
- B) The average of its eight surrounding neighbors
- C) Its value from the previous step minus the residual
- D) Only the left and right neighbors
Which of the following mathematical expression represents the standard five-point formula for 2D Laplace partial differential equation for the uniform step size in both x and y direction?
- A) data:image/png;base64,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.
- B) data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAXAAAAA5CAIAAACgW+d4AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAavSURBVHhe7ZxreeM6FEVLIRhKIRwCoRiGQhiUQRkUQRCEQAiUQTl01pet+urKtqw48nP2+tGvR1bk89K2ksn05ccYYyphQTHGVMOCYoypxm4F5fPz8/X19fv7O9jGmOnZoaBcr1ek5OVOGDLGzMLethwHk/P5zMGEnxYUY2Zmt1vu/f3dgmLMzFhQjDHVsKAYY6phQTHGVMOCYoyphgXFGFMNC4oxphoWFGNMNXa75d7e3hCUy+USbGPM9OxNUG632+l0OhwOqIk4Ho/n8zlcNsZMid8UGGOq8e8Kij5kERxqwqgxe4duD33/8nK9XsNoJf51QameUGM2AZ1vQanJRgVlTyK4m1i0OYOxEeRz9fxbUCwoi2FBWRD5XD3/Y7JwPp8Ph0Py99Bw7s+fP8HYAm1B0R95I7R4kDecDAZjBRQ2wSZqtJtYiAJ/gtEP/uvbDPwMQ7+vpfeCPRe6b0n+H+JhQaGKBH+5XGJvbrfbIkl5hkRQcJ7QKDmDXNIg0Mqb24RbqdFuYsEx/AlGP8fjEc+TP/318fGB+fX1Fey5kM+D+X+UMScUoJZ4Q3Zk1k2KtnqeMPUJOt/yEAKDhCNzo5tQTFqjKuwmFm3OYAyBRPKUCsb9G5iLHIHlc2H+yxm5M5OkJOZSkKA8Yd6dTkFJGjcx50dVz9PXE2ur0Z5ieeaZh3zEb3kSczZUjr6Ej2akoAwmRWfUvmeInvzLPmE6BWWwcfWeqPzMwnxuNNgx3KVwzfImGF2jvlswk4QQTrB7WCQW3kcwGIwWnGgyV9vg1el0KvQNmEkswchCDpnZHIETU4yIhaL0fZeKWnSuJp/LYyxkjKAkWZBng31WjrZ6njD1CXSXJKGkvulUtIC98cx33kiRPtN9ZpGEts+dPFOj9i1IBV1OFCSkYqFniOVRuBcNQKSFvgm5FIwsyZm3swlHwDrtHmNZBo/HY6dv8vn5WyeM2ZnxJ2S0Wjv7Gukrua7SoMFeiHYtdfpo3NbxJI5CL2lXrg8tzqsyL9GaVD3YQyQ+9/FMjTpvoRFe1fkSsVQsmMlIjK6ySLCzICjAL5kF2zCT+cHIEn8ii6zwsEleiAmPxtLZY6xPuvp803h5jIWMERSpLFGpujw65Bm/6KyrnZnxlauFp+LpUPfHTtJJjEjpUBOFyTTmNPLHbsnsqE46ix3DVW4XjCHyiW14pkaZW7BUPvxFYuESI5rchplclUyUU+ib0C2CkYXkMJNA2O3EIn3BZFwejosl02N9vmm8PMZCxgiK6oo3/CQvhIfQxg9z7UymyUxgnKvNqW8p8LadUBWYcKgrpsKk2E0szSVQSdokWy5TbIFIsTeCMQTrlzTBozUqjIXVkpGERWJBVjLHIurF5GD81rRNuPwLIyW+CWUvGFnwH+eZrKaSb3FTVY+lzzeNl8dYyBhBGWQwKZ0RVqd5lAX7/9COjyY0L5R9cCMKH4wWrDZFXQfJ1CjjD4FkBGWpWNiczRGyDZcy+e9jkUBgXCyZHiMKYglGhMarxzjJxiYpEIwW4wr8KGx+tDyTshGCwibkYRKMYvKCMpu8JmRqlEkLgWQEZalYKAqlCUYLdDPjcx+P9kYtxsWS6TGi6CyKxqvHOEn51XbkRe5ixsfgfFPWgruwYTIpw4dHE6qycWotP9XruE6XNOca7hifWjOtMCmqQlOjmL60SKPjf69lhcRcJBY5zINKScaHuEAjto2UsbzKFUliwYw/HOiLJZN5lkoWEazTt9ozTCIoioGfMpHV2G8uUbBgTAOtQH7zKaMGXBWF20B9xuRGHfIwU+sL3YVF4tvxe5OoOUlqFMN4O2n3CP6D7DHIy/WLWCoWGgylax7scb+pBwrrBZof09c/ExHHgtv83jifiaVTUOIOFxpnZrC3IigxeBwrvfYkz7pgT4AepPxUAWZuiEHYck34NAceZo64awbniaXp75XEkvQbHo54l7oSCCTu3k3EMrmgxNBz+tZQsKeB9fXYlHitTVBi8DN+BG2aFcaCcLMD1QxbZyuxzCco5ILtjaBM2nOISKPiuuM6BQWv8I3zbfvN7eZYZyw8VxC4Rd6CVWdDscx6QpkapIq8NwrSCArn8H08poxZObsSFClIJxYUY2ZgV4KSsOa3PMbsEguKMaYaexaU8/2rFpeJv/NijGnYraB83v+LqtjBv6QYswn2fEIxxsyMBcUYUw0LijGmGhYUY0w1LCjGmGpYUIwx1bCgGGOqYUExxlTDgmKMqYYFxRhTDQuKMaYaFhRjTDUsKMaYalhQjDGV+Pn5Cw6199xk5aZVAAAAAElFTkSuQmCC.
- C) data:image/png;base64,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.
- D) data:image/png;base64,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.
Compared to Jacobi’s method, Gauss–Seidel’s method generally:
- A) Does not require initial guesses
- B) Converges more slowly
- C) Cannot be used for PDEs
- D) Converges faster because updated values are used immediately
Which type of PDE is typically used to model steady-state heat conduction in a solid?
- A) Elliptic PDE
- B) Hyperbolic PDE
- C) Parabolic PDE
- D) Ordinary differential equation
Which of the following is a key disadvantage of the Crank–Nicolson scheme compared to Forward Time Central Space (FTCS) scheme?
- A) It is only first-order accurate in time
- B) It is conditionally stable
- C) It cannot handle boundary conditions
- D) It requires solving a system of equations at each time step
data:image/png;base64,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 .
- A) Liebmann's
- B) Gauss Jordan
- C) Newton's
- D) Gauss elimination
The Crank-Nicolson scheme when applied on heat diffusion equation is ……
- A) None of these
- B) Unconditionally stable
- C) Conditionally stable
- D) Neither stable nor bounded
When applying Jacobi or Gauss–Seidel to the steady-state heat equation, which factor does not affect the number of iterations required for convergence?
- A) Convergence tolerance
- B) Physical units of temperature
- C) Initial guess
- D) Grid resolution (Δx, Δy)
Fourier analysis method is used to find the …………. of finite difference scheme.
- A) None of these
- B) Stability
- C) Consistency
- D) Convergence
Von Neumann stability analysis involves:
- A) Minimizing the residual at each time step
- B) Representing numerical errors as Fourier series and examining their growth
- C) Analyzing the eigenvalues of the coefficient matrix
- D) Checking the positivity of the solution
Laplace partial differential equation is a type of…………………. partial equation.
- A) Elliptical
- B) Parabolic
- C) None of these
- D) Hyperbolic
A finite difference method when applied on PDE will be stable if the amplification factor G is ……
- A) Unrestrained
- B) None of these
- C) Bounded
- D) Unbounded
For stability of an explicit scheme using Fourier analysis, the amplification factor G must satisfy:
- A) ∣G∣≥1
- B) ∣G∣≤1
- C) ∣G∣=0
- D) ∣G∣>1
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- B) data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALgAAAAaCAIAAACLhQF1AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAoBSURBVGhD7dh3tM/1Hwfwn4w6ZjQVEopK2kUhDaNyzHQooqF10kA0hKym7GSe7HE69ii70t57qE4TkdUiid/j53V/n3NP3XvdeyOc83398T3v8fq836/xfI339z87UpSibFAKKCnKFqWAkqJsUQooKcoWpYCSomxRCigpyhblEii//vrrwoULb7vttuuvv75v376bNm2aN2/eXXfdZTp58uStW7em8f2N3nrrLTw4v/vuO9MvvviiT58+vt2yZUsw7EV69dVXO3bsSLzPPvssbSkjoiy29u3bL1u2LG3pH5MzR40aNWTIkPXr16ct7WOUS6CMGTPm4osvnjZtWufOnWvUqDF+/Pirrrpq7NixV1555T333LN58+Y0vr/R6tWroaRUqVLvvfee6csvv1ytWrWHHnro559/Doa9SCtXriRbwYIFX3jhhbSljOj3338fPXp0pUqVhg4dmrb0j2nVqlWtW7du0qTJt99+m7a0j1EugXLeeefdeeed27Zt27hx4/Lly6+++uoOHTrICj/spO3bt6fxZUTPPPNMApTffvvtyy+/XLt27Z9//hm7e5cEQLFixbIGCvroo48uuuii3QiUP/74Q4r95ptvskjG/4TkSIHN2mnznFNugPLxxx+XL1++e/fuMX377bdPOeWULl26xHSXtHjx4gQo+xqNGzcuO0Bhgbp16+5GoOxpeuqppw499NBffvklbZ5zyhQoQhwC5MMiRYq444orrnjttdcsAn7Lli0POuigAw88sHjx4i1atGjTps0BBxxgWrRo0f79+2tf0o74PwmXWbNm1a5d+5BDDjn66KMl2ADK119/LRXly5cvKT1+n3zyyUsvvbRw4cIVKlRQy6KKyfbdunWT7QnjItcpEI899hj+77//vm3btkcddRQh69WrJ13Jcz5RCgsUKMCdixYtqlWrFtnc++GHH9qihcF999130kknWb/wwgt1J9ZRZkCRIwl83XXXhTV8cvLJJwdQbEU9LV26NINUr1590qRJVLalLuO34nxK2W3QoIEEPH369LPPPps1brzxRqrJxI8++ihpo/QgzMzywAMPTJkyhdY+xElTZzqZeHfccYfriNq0aVMp2frEiROPPfbYPHnyfP755zfddFOhQoWOO+64qVOnEm/gwIHMbosw9K1atSr+nFKmQHn33XcrV6589913b9iwgSjQULNmzTfffNPWBx98UK5cuSSj6E9xZpZReAVK2OXxxx8Pv0JMklEiNBOg6BBvvvnmNWvWfPXVV9od/nj//fetP/LIIwcffLB7scFilSpVnn76aetKOzfUr19fe6F+6TFdtGDBgihkBIa2kSNH/vjjj5wnCw4YMACMHK6vYkTjJUuWEJ4bItoyA8qKFSv0UqKCNSRwDTjTB1Dc26xZszp16sA9WD/88MMnnnjihAkTAq+Cigz9+vXTpS5duvT4449XtWfOnOkrWnNbYNQuVCU9Cgscc8wxOGfMmCHweNqHQGPLIZdccskrr7wCMYyArUePHtbR4MGDWYnLBDPDQlujRo3i0eCFcdhhh+2RjOJ6YRpyI7YDYQ4zzhFQWITvmQDSY4XCCVBU5caNG2fYzD744IMnnHDCSy+9ZNy8efPLLrss1t95550LLriA7Yy5n61ffPHF2GL0c84559577/3pp59M+VVNjC1dhRM0UjwdK0HsKPc4P+I1M6CIeOqzfkwJf9ZZZwVQ5s+fL5T5LDozQSUS4AM6Td146qmnBmhcITELADYxlaFLliwJqcbUp28CFATWt99+e4y1/BQhQ0wTYtLTTz+deWPKGrKdh6QxTHAWqL3++uumexAoDRs2POOMMxL/ySXQ0LVrV+OsgSK1eumNGDGC0QnNuCLeQzqsg9L3KH8BClt/8sknUgLFJNUEKEzGUkJWGM2dO1eq8M6yLoUogon+0CCMMIeTAEXwJVuAQozYch0LOkp+gq1dAqVVq1b8rcTENH2P0rdvX0XE+bElt2G+/PLLI5QBBWcARf5Tatu1a7eT8X9oE4pZAKV3794xBhRZKpmypNggvMRWpkyZvwAlSn8AhWphwD0IFPU+d0CZM2eObGSXoAoHYin2WrduXTBkARTJhu+HDx/Of7r0BChShU+uueYat7C1Cq0WWL/11lu1LEkzn02gcBgJ1Qgtnse8bmOXQJEJGN2DLqbpgcJbEj58x9aeBsqnn36quAwZMoTw1JGT9jJQCEGNyGMoZNVnGOeo9ES3wWcGsSIZZAgUd+m/1JRQNX3pYU2u8naVq6ZNmyblhulVZV1b4lfdt771/vvvD4tkBhRWlp+ijmSz9GiedAPJH3HK32mnnRZA4R7qRNtoSiOdgUdA1LjdDhSf64iDLcPSkwVQgGwnY24oU6BQgP633HLLpk2bKM/EOoM33njDluxStmzZTp06Badaq1/T9mvgYyU9WYSD6MWMuYdjdIJRO4kudekqmFX7nDdv3l69ejErLGqf4e/555/Hpo1P7JueYIv/ZBFVScaCXV3qs88+G80sgZMeRWLTOjhH+RCRhx9+uG+3bt3qlaSQK3OBYxVT0+OE+Cqh2bNnUxkEjeWVnj17VqxYUdoz5bNzzz0XQCU57xcoPPPMMwVDyAAxMlYAhRn5GFYCQ1Q74ogjJAZjK3IbWIcv6eK6pEcBXJEpnROYss4Hd8YUNt5E3mLxv/YTTzzhfRSxrUsjpJrw3HPPmS5btgwovRNxirdc/P+bKVCcCKHsThTPSDFHMYJGWOgMFGYIUC+vvfba/Pnzk0OEZZjcBCKcOYTnVHSI8fbjNgdS3ktYHPCEUJCWON5DBpsAYqwIMtYsUaKEE4LOP/982opCDtBLsj6kegoJZc+EqEQeOKymMEEeu7hI7pGoHQXZzC1kJbNhw4YpdsChgrCpp6O3N9cmrXcQ2bxcZDi386i3KAi6VA8LED6UNR0I2Z4/ZAs7gAsVvHslJA8iIU5ZkW2gVJGBHYgElx6G7GkX1kXmDTfcEP8+UIfB1TIWdt3ChQu99r3swNQiMSRaoB89erTq7F0m0qQ6ZhEALMlNYkPWZBO2PfLII9lq3rx58XrPEWUKFOQ+CpMbPN0UIeKX1Swiysu3yRS2Iv3+hSzacgjXGpASs7GBE+Lb+EdSlGBD2IzxEEC0samSFJygKZS1lkzmE/KQzbqvSBKxi+JG6yFkXGTFscknDjfFGWzkcWOwhbLpiYSxG5y+xRZiY04UsZ64IdSx6LowQvAYJLZFDkExDmkTk1pPDO4oJ5vGh37thiIuSi+8q02Tq0MXPKZ4EhPliLICyj5CmhIRz4KhsF8QkVRERjCk6F+g/QAo2hplpW3btvChd/FoUpW9d5LuOEX/Au0HQEEeVjoDzwfk5Tlo0KB4fKboX6P9Aygp2uuUAkqKskUpoKQoW5QCSoqyQTt2/Be9AtK6KeB+TAAAAABJRU5ErkJggg== .
- C) data:image/png;base64,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 .
- D) data:image/png;base64,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 .
The Laplace equation describes which of the following physical phenomena?
- A) Fluid flow with time dependence
- B) Heat conduction over time
- C) Wave propagation
- D) Steady-state temperature distribution
Which of the following best describes the purpose of stability analysis in numerical solutions of PDEs?
- A) To determine the exact solution of the PDE
- B) To ensure that errors do not grow uncontrollably during iterations
- C) To minimize computational time
- D) To verify boundary conditions
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f0ViMmomBjCgv7Oo38f+v34v6vrDx7mLeDKwxizCbmwVB7vFoawoJQ5BJPolYe+gpQqTWWH/krX/z2LeQv4vDDGbFIqD/0Xof3PPkKHxOmfXYJSeeiHqvJnH1F2cMFd/7mMeQu48jDGbKJ3dP3xASXFw9r/UCmNQOL88d//i2Cjv4DRf0Cr4JT46M9o+FeN3NX3JILsX6/MHePKwxizCRmRLEhhQYIkL65+z1BFggKaLjsKX758ifKC6xwf/TdBRDX+qlT/LQzB9Hcjc9+48jDGGGPMebjyMMYYY8x5uPIwxhhjzHm48jDGGGPMebjyMMYYY8x5uPIwxhhjzHm48jDGGGPMebjyMMYYY8x5uPIwxhhjzHm48jDGGGPMebjyMMYYY8x5uPIwxhhjzHm48jDGGGPMebjyMMYYY8x5uPIwxhhjzHm48jDGGGPMebjyMMYYY8x5uPIwxhhjzHm48jDGGGPMebjyMMYYY8x5uPIwxhhjzHmcVHl8+PDhn4Xv37+Ppr9GBuH379+j6eX49evXp0+fHh4eNMRoPcwl5rvFt2/f3r9/r+G+fPkyWvdgdqULU1YLqOXO+PHjh2ZHuEbTAXbD+5dbxZgrhG2v/cxRNprWDo3OmUffJbh1/4HV0RQ+f/48mq6P8w5KHd+TKkGZ7+PHj0PeA1PoPymLHOTnz58kEh4zrr9+/fru3Tu1P4nd+b4Iynk4zED4yXkxbhyAfYmH+QG7XEgz+InPQzgXJssEtbKBDlkWesiJ3fC+yFYxp8FKsdas2pBfg2vwodO90sNSslc/NDrnHH2XQ/6Tj4Z8g2iZnpQOTua8yoNacp7SJglgC/QvUdbhKunk4JPDE7s6r935/j16iT/+naOg3ZmnqcrjEiENnlpfviyKWNljW5ngSHiftFXMq3Nm1ctYq4/SK1beE7pXqjxKkdEPjc4JR99F0UM9hA22FvdK0GePay6ezqs8CMTLLpUSw7z6fgZPTY3sUVLXEBIvPt/OX7488YDx/AxhQSG95kr5L1F1ezBiu+F93SrKXDNsm1t/lFazVz80OhyJ15yVd2GC84f6+hf3SPH0upxUeWipXrZK4M0Vmy/7uok15Zsjn15Cub8WX2K+BaoE9tbfbC88LA+YzppJrr11tF5DmLIb3idtFfOmIFvriz27aDTdIKvZqx8ahROOvoui14nJl86bWFwW7srfiJ5ceeitEfKBW6pjtqx0oiWqBHYkFSXX6OgW6FW7NApuEUHdJZq5lKZd3/QYnVsoTLaLwB+yhZRxo+iHG8Hkm2FXhqiC5/MN8uxQiHDtEhEO+qOejTORoiD/S9bEbD9rtoL2jJ2ga9Bd0NqB3MOUwrX1zsSgeuzpQl8cK4tYwGzoo8x1Xgh5C8XIbngPbpXV9eVoln15ghg6S6dBCTumaIxyhxYUEAnUn/A9PPQ3sGwB8sRh1bctspMoMxZmdYvIaMkUQ8wq4KjhnnS4tfi4ucoHY5J9ZpS8KGEBBbUwulqkpmtQJGHLc/6lLyi2tJTHBCYBiU2VUXi7D4Kx6CVnsMOq0aJbR8KbecZTueUVLRFMgQKNPRoZ7qKDb+F5d7XMd8sgOop/Xmh8poUQDXkhrAEX5e58OO7GY0JsWXQuSigCRbKQnx06bm3RjAZFB6/ojhibTQ9yLDT/ZvsiT4drTPHvuLdsTm7FNDUjiMdNZFdZoz7KRXly5QGaSZ6q9m6sFnFEJDQSgdAQwQhQX11WqNgEPUX0wqBs5thphzG0VlfrpFursB6sE7FWiBkLfS1zRnMZwh5auSEkducLEUamxi2u0R/3DqAuJWKBQifjID/z3tIBUVwiPkx/CAvzoD11J0iMIfAB1IgRpo9Iu7xlaKkFKNAuHfzRs9dXMCj7R76ViK0uDczDK+ZbZXV95QbO6y5zVCNihAXwPMLOXa4VQ5QxpYeFf+mCiAJ30VFfoYWLY4sL0C1Y9W3caxRT9EJf/oT/3MUZ3JYoD2VzWeSVVZYPdOHWwZjIAregbGnFSr5hgRb6cg0oSwcnEXW95Tm+oaOhI7bRS0wCEqCQnQ+yD0I+AMMh5uWYO6kwdmJxh3zgfMY+LUNYYOhiBDRu2FkFD7GGq3Kvu4plho75yrdYx4AuIFdzJLUNskHFX9awg+U8tflwii2Lpbvat6C7W2wt7nyLZogSI64+yLSUhS6rwC0aFQGMRxfdBbmhGYFGYVdIFLFJGAVNrjE77p3CTohXkaMRDlxHhJgqIOZYEB1WKyaf94qINRjy4ygs3pCXTRM2iTh3sRldtKV03cFJlHGDi9G0ONk30GrjFthk4w4hsTvfvqWeNC50m0EPnVrycHoqhrDQz5rdoBWzuztBCuUZABoZJU6T1akpYqEDWvHVBxt6EGQ27zHQE5gnKFZ9KKCwtWS76yv7tPShtRBZWTMdwuPUiBiaaikK2CwLx3Bxsjxp73VTGr2cU3RHJzeiUx4NWtCJzSA7eTNMYtJXUy15FqDQMUHaGT3iI2gpLkHxXGaZMhdq2Y2tuuS5y42+z6H7IPvZ1TIiyMmY/urcg3IXPxEhZgSI+XzuXmmT5C7QD40OfhKfMjr+hyiFiB6afaBA3fO664Et4Qr7wLxCf3c4OhZriCUUha3FVdh3t2hGCgwXDsifyULL//kxyFakRddYJgLl0HvSCXAhdrbRKgpHPGlMg9jREuFgnsxW16Ddk1v67lFL7A/oAc0wBHfz044P7LAhNLRg+WEDWkq4tasmeyWj6qdvwd35oqDDSyIopHk/7TI5BXro+g7GgTJ3bUc0h3wgaE/dCVq18hjISHZGU8ubAUrEgC6lJdOD0PcY4DAMITEJr5hslSPrK/dytIPiuazlE03rUlYzz2J14cRT9143Jf2+KzCbY6uWIaytslryvI7HBNS9x1+hKM4AIvr9aaUxKzMvWvLBQqxyuI4EREbKPofug/rm4UCTHcICYnZSj2q3L4rN3adyNTKr+x8f8gp2dCSWB4qW6NWjxy3MDqGhufQHZwgLcjVnk2A+XA/+1ibJbC2uHDuyRQO5lxVYl2xEY4X/uIfzee2AcUsL8acRZSxznV2CbqQH+QRmZ+sEHGVuXDAN5lBCzK282CxSDh/oaBjCAi05FtrB+VQqKItETLVjJvrYRwG1IT8OoVkE80e6ULZFsDtfddT+5oEhbtzVXpHCEeiC2SEkFIpySyPGAmnu5QHjCaQx+3AkaCGitrsTyqoJlGnMMcdO8V8hLQ7TsrXiq4uLmPcYKFbl3Bdb4Q0mW+XI+qKwal+e6xbXmMJnyAcrptAJa+qSg4N+3m+Zp+49TKE/hAWtV/ZHi54dUGBz/Psqa01pH/J2TGSt3CpbOlBwsntCw+XdCN1zrmmJLarY5h1yJCB6lMJI0H3QcGUXlSG6k/1RLXBXwUcHa089n4FeJeB9m3W6KQ0dAdTU8ApQxhO2Xxk602OLmPcVcBcjtKOM2dG6MB9OYcRDiSBvJ/7A6uJin8aDWzTAHxToK1FGIlZQxlo1SEs+BmUk6OslI2ondFibnwAX4m8rD/zWBS2KCBNTS6CnK8Kn0PRg5YhrB0/WjDVmVw3hUX9StXH3yLbAKxoPrkGZV7A7XykIvOIWzox7x2DH0Fe7p9DPKSjPmOZeBiWeOaQg94aw0IOGeHwnlFUTivkQNg44DNLIKg95b8UVhOxnXwWQkR78SXiDyVbZXV/Zz+4FckkQKwLIHMsoOimG8LgoERzNtEQ+2PWtgFpfRBwYwoKKsHyCaxY5gGWVQZ6E25OYHNnSgrnjHu19XTRceVq752WLKrY5RIi7ASlGgu4DpmjJ3mr/5yG6kxhniCGsERaIpy5oUWyZS/G/eyUf8oEMPRQdmcrTkfP8y7V2ptAeRr+sSAGdHFvtq75JMIImtwhLjL47nLoMYUH+sxWHvMbq4h7fohl5NYS144iB8lhMvBhUF4VXRAvTx37fJ5qj4O7uCXAhnll54DFoblpLAkQQaeGibCba++5ZDdaQ1zJNgbuEbAgHdgx38xqDjsLSBT/zSs8hAlgYQmJ3vijQMn/k5mANC6s7Rs9AeTjxJ7ukcGUH9JSWs4aW3aAd3wkaIq+aoCMWhtDyqOiPnGK49VRLPwdBLXkVYGvbTMIb4PbWVtldX9lf3d7yczI03qKQzzgdcIRXojZAVsg8ae/JVN4DaimLqF0xhAW5lANLuLIdIHp5T05iokHzagJ9c3cgAmwkOdPtcKvog5QjdICYZ1eelCMB0T4vkxXdBy3HEBYUh7xRi5M4g7i1voKBgC4MJ+e3nkroXunIKpuwhGIVTJWHgpZwXrEqh8wc9HMkFS7sDPm/6OgI+7vDcReGsCwccSihKKBDl764Gmt3i2b6g6xnP54ajZX979NXS37QZEQ6egzLkqnLfB1P4JmVh7xnYhFrWoCHJD8zAk1uDeG/oRG9RXto6/zty4x9WoawBnezD1r13AIsBo35EJmTLfCshrfFcp+dnmE9jYK786OkoC2VN1zQg6OzbB6u3gto2Q2aTB3ZCatDKOb56Vp9WuhFY8SQUPNI0yKxo/0TY+G5TsCwIOT8EBKT8Ir5Vtld39U5Ch36OXFiBz+HsPZocNbn476HNPOkvSdTMTq9lAXLIpa10D7Jwek7p+fXSUz6zulbGt9YYgblglt9RjRmB0QJXR+ILjl5HAlIMYInManuAyKNQ1gM4g8jcjGampN9A3RklpCGG7QA3panErpX9KKRiQx5AZ3s6irFlDZz+LC6NLi0uuhQIsmUiQMtERw65shAdmB3OFnTNRAuWkooCluL23dO36KFvo4lwrLZn5FYF27pWJMospHVrYLPNOYNhsESpRPY2Ulb6HnLq64J92XrS8I1LbSzLzXh3kJcePywpgBxcuVnJvQlQoSbWyXQQgrqwr8YZ81y9EHr1J/MLTACGMFgWOMaI/P5Zh16MSJ2JnmuQ+TpMoT/gkFuoaBHAuOMVfJQD1e4pFAvWoeC9oydkIfoz4a6KywKEUhN0aOd6WABZ3S3w9zDB8blAlO0cA0RDY3FRcRBTMIr5M/WVmEI7sr51fXFfo5YRsvH7BRn9gxi9k2nT5yegKh14RZD08K86CUd/sWTCPiubwWFAk3sYFYTpzuinOSCFtDQ/It+2SfqhSm5xKCIZU8uIZnFZNKdW7KvQRldptBRF0AB/1HAbTXK82yHedGiiQjsyBR7T6uAOA8IwdRYKONqRB66DxpRy0ELnpfl2HKSjYGf2XiGdnTkuWBcjT7khNq7V9iPIwtkQXfzhgzQRyH8R0c7QXcFRvBKo6DG3bINMiWSaMoxXEXkGvcQuZa+Nkb2bT4c1+jjNga5lsMKBWJehaC4FPGnC31jLHmSx+podOmLsCy0tfiXQdWuFibONUNgQQstEbjIRjCOiBruaV40aplkhBZ6lS13Dn+cfgbaAcxhyEsLE8hxFEwMTbbIkJfFQxPY04pFtChGUqMLC0lfIL55PyncoQlaEvQV/Q7KWmmp4W3uLqSQJzWHQfGZLtntI/MF+mp2tOfuR9B+ynu0oJ2KDvCw5dCJHi4cQJPGOH3UuBu04zshDxEbnZjQEiIQuiVa//8P84Q05QYiCnEmrqLVkRpD408WQyfbFLvhhd2tMllfrmknCENuEA0FSmo5OMAtbA5hQUvAcLHrygZglbMDE986mJJybIyyiIohUQ2b+FNsKly0c5cLNOk17i0cicnWltZ60RiBIg60MFZWkw+oRZSklk8MHKAlO6/HOTu8GxDQXlUo1CK6DxBh4V8UZDPoTqIgByZrpy1x5KmE7hUTQRlWH5bsTIYhMMW/co9/uR73HsGaggwlDqsokmEKfTkmkQliTcPJYN9Xk+G4q03FLcVKw4W4ytbiTrboKuhgZAhLdzpifMiLe5pa3hUREK2CtkfEpxuRPo7F5gR8k2UcmOyii/LMyuMuYTHyVrhadARsPf93Bk9FPwj0vO0eW8/jSHhvZaucgPLW/PAiXCziEIwxbx5XHgOKSg5QjtEhXzE661dfX+4PTXYIj5DGSGZDeGl2w3tDW+UEWIt5VUFRQrjye5gx5o3jyuMPHI4fP37kLfb60zlv/2/qHFcdEJ83fi5/I8JK5Y+HL8hueG9oq5yAqooP01+m9IGqf3g3xrxZXHmMk7H8Enad8HJJzntThzi5jeJDv0oC00e8UNbfDe8NbZVzUEAI2uTHKf3SzApOfjs3xrwpXHkYY4wx5jxceRhjjDHmPFx5GGOMMeY8XHkYY4wx5jxceRhjjDHmPFx5GGOMMeY8XHkYY4wx5jxceRhjjDHmPFx5GGOMMeY8XHkYY4wx5jxceRhjjDHmPFx5GGOMMeY8XHkYY4wx5jxceRhjjDHmPFx5GGOMMeY8XHkYY4wx5jxceRhjjDHmPFx5GGOMMeY8XHkYY4wx5jxceRhjjDHmPFx5GGOMMeY8XHkYcyk+fPjwz8L3799H08txUeOvwpcvXzSjz58/jyZjzD3iysOYFT59+kQK/Pnz55Cfy/v377Hz69evIb8oMv779+8h3z7UHMzobmqpVX78+BFV48ePH/9+jxlzc7jyMGaFd+/ePTw8DOEvIMe8iJ1VME7xMYS7QJ897qmWKlB2MEHqWq6pR7XNLlSYGnO1uPIw5oKQWnivHcJLQw67sx8mbrqWooBgOebLzX6AIfz777dv36IQMebt4MrDmEtBKiKv8B4/5Bfl58+fGL+zHyYeHh5urpb6/fs3BQQFEyUFaz35gKElKxOk5XJfxYy5Tlx5mCuFY1o/h5eXYP0Fhs730OFfRBp540QkB+jnc71TwtevX/90XtAn/cgQshAtIf748UMK6JMbQGkeU9hHoedIkhDuocld3EYh21kFm2j+GW/JQPifUxcGGV3DAZqaF+AGLShgQQoKQkFJcen9/3frrbjhgOzHHFff4FdtZjCou7m7fmigr0StQm5haESmE+7hQ46GwI68BdSksDUjLGhGE7JBInC89MFV7Ua6a2/M0ZT5d8gLiuSuk8bcE648zDVCQuU0J3/05E0uIT1wUXSUexABBdSkr7v5uFeKCpvYQQx9UDLQNTkYpIMRMg0i7cpVOWGgQ0eGlmVSEQqgu6ugiYJ8o7vSGP7rbjGoidCouyhzl3/VvQcKTWZKd6V21FDgmvbVuHGByHWZ4xGbupvR9FEe8lreVZxjvthBZGjGZSBZyPoQq4mCooe38xlxa3ReQ4PKCHCNkXFvAw3EhgE8Cf93kXs5noCrvdGY+8aVh7lqIpdIVG4ouUQpTelKLTrNJSo/RQKTBchnPWJOn2REGMIj6JBplJJBg2YjGjRcBcRuJyMjQ1hSGkl9CM0gY+GAroFrlCNNdn8ISG7hAjHiAOqS44aIzdB5hs0Mt5jCEB7rjKzMXVL+EB6/ZkWXbpzgl5YyhBymJc8oKxQ0RN5OKK8WUoJbmgVdjnzkKGCcvjmesNpozH3jysNcNZzLORmvprp+dqtFOVtdIsORvZQ8ooYgheSMrtKkvPjKCGaH/JiDI8OVUWDVTkGpNDzJdIMZGc9ulxKtd1dWzoVRiRt1T7GpUiDe6Y/YzGRr6LCOiJHmNYX8wUDrEi365hHBQV8WJIL8ydErM2JQxMkSSD/7MAdlHAj7T6W4J1YbjblvXHmYq4ZDOb+SKtWVY5qW8mlBOWwIiwLnOxdkL2UOWqJ84VZ+zVXCKy++Gje/5mInD6oknR3TKJMXaMAfucocS/6Twa2k3p3ETi7R1F0O44nEkoNpyVPoNpkjDOGYzYxyqq6ZIDGkBdSCiAVdgwqR3FJqKRyL4WikO/PFGh2lACjkGalLXrUMAedu3l27YDDWa8vsBHp1f5gCjXnnGHP3uPIw14uSd36p1bk/hAW910YZAcphOQMhKuEp+alFXcglkQuFEl6pA5QzhvCYtHLSVf4YwkJJnFvgrTTJo1m5zzRTnNSUcxJVd4FvZPSS23rcik3NMZcCuzYLERPUmB1O0gK0YFwti+Ifet3DcLmWknuCW0w2K0OfER7SkkfJaMSsfxCcxxmVZXSPiO2Cch9RUdpy0pi7ZPNoM+bV0Ukd6U2FiFJXoB8scgrUm26pV4DDnUymPEHOwA4tXJTMgWZOeIIW2oew9jKNCENYSgG6dDtbkDVRxpkhLwbziAWcz8aVRPOUEbO1juKWp7BqM2f3XZsF1QqEAsuyo1KAC1ry0KC1jtqLXoi5lqILLZM032eEt5MYasTixpOgr2aEn0fsoINyLuaAlidF1Zg7wJWHuV6UbHStBEZqJJ+pRehrRFQeKiaAC7WA7HDix+smLUDfnK0FmtwawgLZTt2H/JhBcxZkRFqGsCjQUuwUUMgWUM4W/sxhOyEVJ0uJBmTcknTRydmxT2HVZvkMM7dZkAUGCrNqIea5pBBl+qoy0R9yqmOGvOjkzVBm1FetoPIxl1bPA5cwQmRYLxzOIS2gyQbO5V2fpjFvAVce5nqJqoLTnMykz+kkG4lKQhz3cXbTTgLgZM/5EmQnJ3LluciIGbVjnF7KIj1FqTs6JFENrbSHqzRyjTJuyA5i8QdoR59bXCDSEf2cJjGLgvI6OsptocytnK6kTDv6SsbRwjWzwHJ0F3/qmhSQbpMutNCXoQ/aLOgjhIyoRRaYae9Fe16O8IfQqUzJHtId42WhV2dUdkuGllgjRA3UK9HjMBDDydstFBOtO/oEcB5DY+4SVx7meiEZkEs4qTnNlWOU8vlXIme37qodONMjzwU5ZQpayDpdE5RxyQfxNk86oSUnOW7RHZQIgeQhH+iogdQrxAJDK3OjA0wTUzkDcS1PdFcZVLeUvfLHBnyTP6iFEa5pUffwU6BDe86R3SZuy2Z2bGKzo9yf1dSSRxH4TzvGh7x4qODgZEycGkj7AR+UvNUOfUZQdksHT2RQfXNxeTkI9dYsjHkjuPIwNwypghO8ZzJjjDFXiysPc8Pwlkzl4bdGY4y5IVx5mBtGH+SHYIwx5hbwqW1uFf20D5+2//sFY4wx14YrD2OMMcachysPY4wxxpyHKw9jjDHGnIcrD2OMMcachysPY4wxxpyHKw9jjDHGnIcrD2OMMcachysPY4wxxpyHKw9jjDHGnIcrD2OMMcachysPY4wxxpyHKw9jjDHGnMW///4PM+yiSIbtzDgAAAAASUVORK5CYII=
- A) Backward difference
- B) Forward difference
- C) Crank-Nicolson scheme
- D) Central difference