When using the Gauss-Seidel method to solve the linear system arising from the finite difference discretization of the Laplace PDE, what is the primary advantage of this method?

• A) It is more suitable for non-linear systems compared to linear systems.
• B) It does not require the solution of any matrix equations.
• C) It requires fewer iterations than the Jacobi method for convergence.
• D) It directly solves the system of equations without needing an iterative approach.

Which of the following is a correct update formula for the Gauss-Seidel iteration in solving the finite difference equations for the Laplace PDE?

• A) $u_{i,j}^{(k+1)} = \frac{1}{4} \left( u_{i+1,j}^{(k+1)} + u_{i-1,j}^{(k+1)} + u_{i,j+1}^{(k)} + u_{i,j-1}^{(k)} \right)$
• B) $u_{i,j}^{(k+1)} = \frac{1}{4} \left( u_{i+1,j}^{(k)} + u_{i-1,j}^{(k)} + u_{i,j+1}^{(k+1)} + u_{i,j-1}^{(k+1)} \right)$
• C) $u_{i,j}^{(k+1)} = \frac{1}{4} \left( u_{i+1,j}^{(k+1)} + u_{i-1,j}^{(k)} + u_{i,j+1}^{(k)} + u_{i,j-1}^{(k)} \right)$
• D) $u_{i,j}^{(k+1)} = \frac{1}{4} \left( u_{i+1,j}^{(k)} + u_{i-1,j}^{(k+1)} + u_{i,j+1}^{(k)} + u_{i,j-1}^{(k)} \right)$

The Poisson Differential Equation $\frac{\partial ^ 2 u}{\partial x ^2} + \frac{\partial ^ 2 u}{\partial y ^2} = f(x,y)$ becomes Laplace Differential Equation when

• A) $f(x,y)=xe^y$
• B) $f(x,y)=e^x$
• C) $f(x,y)=1$
• D) $f(x,y)=0$

Poisson’s partial differential equation is a type of…………………. partial equation.

• A) Hyperbolic
• B) Elliptical
• C) Parabolic
• D) None of these

The Partial Differential Equation $\frac{\partial ^ 2 u}{\partial x ^2} + \frac{\partial ^ 2 u}{\partial y ^2} = xe^y$ is

• A) Non-homogeneous
• B) Heat Equation
• C) Homogeneous
• D) Non-Linear

The discretized form of 2D Laplace PDE for the nonuniform grid spacing in both direction is given by the equation,

• A) data:image/png;base64,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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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.

Gauss-Seidel method is also known as………. Method.

• A) Gauss Jorden
• B) Jacobi’s iterative
• C) Successive displacement
• D) Gauss elimination

The rotated five-point stencil differs from the standard stencil because it:

• A) Uses only horizontal neighbors
• B) Uses diagonal neighbors instead of axial neighbors
• C) Uses only vertical neighbors
• D) Uses all eight surrounding neighbors

Which of the following equation represents 2D Laplace partial differential equation?

• A) data:image/png;base64,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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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.

Which of the following advantages does the Gauss-Seidel method have over the Jacobi method when solving elliptic PDEs?

• A) Gauss-Seidel method can handle non-linear PDEs directly.
• B) Gauss-Seidel method requires less computational effort per iteration.
• C) Gauss-Seidel method is less sensitive to the choice of initial guess.
• D) Gauss-Seidel method generally converges faster because it uses updated values immediately.

In the finite difference method for solving the Laplace PDE $\nabla^2 u = 0$, which of the following approximations is used for the Laplacian $\nabla^2 u$ at a grid point $(i,j)$?

• A) $\nabla^2 u \approx \frac{u_{i+1,j} - 2u_{i,j} + u_{i-1,j}}{h^2} + \frac{u_{i,j+1} - 2u_{i,j} + u_{i,j-1}}{h^2}$
• B) $\nabla^2 u \approx \frac{u_{i+1,j} + u_{i,j+1} - 2u_{i,j}}{h^2}$
• C) $\nabla^2 u \approx \frac{u_{i+1,j} - u_{i,j}}{h} + \frac{u_{i,j+1} - u_{i,j}}{h}$
• D) $\nabla^2 u \approx \frac{u_{i+1,j} - u_{i,j}}{h} - \frac{u_{i,j} - u_{i-1,j}}{h}$

Which form of the finite difference approximation is typically used for solving the Poisson equation using the Gauss-Seidel method?

• A) Second-order central difference
• B) Fourth-order central difference
• C) First-order backward difference
• D) First-order forward difference

The number of grid points along $x-axis$ is $n=10$, For the solution of a PDE through finite difference method the valu of $i=$_____________.

• A) $0,1,2,3,...,9,10$
• B) $1,2,3,...,9,10$
• C) $1,2,3,...,9$
• D) $0,1,2,3,...,9$

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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 discretized form of 2D Laplace PDE for the uniform grid spacing in both direction is given by the equation,

• A) data:image/png;base64,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.
• B) data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAboAAAA1CAIAAAC4BLlrAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAk4SURBVHhe7Zphedw6EEUfhWIohXIohGAohTAogzIIgiIogRIog3LoO81V9WklWR55dx2vc8+PfDuyLc0djUbybv77Y4wxJoDLpTHGhHC5NMaYEC6XxhgTwuXSGGNCuFwaY0wIl0tjjAnhcmmMMSFcLo0xJoTLpTHGhHC5NMaYEC6XxhgTwuXSGGNCvOty+V/B58+fU2vBz58/n56enp+fk20Oxrdv35i4Hz9+JHtfvn79+vHjx9+/fyfbHAxmhznqTlBa9q90136XaLlkVPrlb7JPwThSiP3w4cPLy0uyzSGhVrIqvnz5kuxdYB/99OkTW+mvX79SkzkeFErOOqxi5is1Ndy+XDLY3yL8nsrlapTNcWBVULx2q5iUSHJj5wJtNsOJZ7CWB0WgJVQuyUV4P+WSAwuXTnmu1FtCMk6EdnTezZMdY1s0yBnOs8k4EUr7t/pm467wHrD0tQmSb1kuSSlqpRLrnZTLs64HOGu5BI57HCKmvkncEI0Tb6UnLpe8ECCtW75ov1m51KbN3/dTLredUx6FE5fL79+/z07chmhwTqEoJ+NcnLhcAme+7sQh+Tblko1aPy3xuS2Xz8/PtEAZX5K1bNFTcMwfl3GsjZR0VUlDKF511PczAWWL7oGpM86exAvEI0rGjXZCB8SjIRSTdgh9VVV1RWEtW3hK91DWU9PBmCqXDydZc92qozGeM6NcoXDkF34Nxl9dEgpHuZ/zQlS1dKvPleRpGFN528I9baTUeTIKlEzlBqUTftmytJyOw1SBeDjJWsPJCDAVDVBA2rwiCMSES+XvCaydqkUHHC2oAyJ1waX6cJL18tHOHY3x7F3MlSp2SqxqsLZRESxbKKCHLR/dSNGIimRcwiVIxr+jdNmiahJMuDdBU5aMAK/6HkYys4kzuJTsNWajofvL00BGQ+c46CudsgXyu9oxwdXK4TGPJVnq2v9noDFeoPq5wm6AzvINWonCX11SY1WwX15etL3kB7UFleFTP8lYgBv2+S8NBuqWy6XwVYcXxEpv3jxRVz3L1Ryfe8Bw+JCMBkV7lUG6HFCyRHVrIp5waWnBXx8N9dDtv3qLIoEVqPweyqXqnMVAg7GAR+jhTj8rqfMI6YGGDZIVwGT0uJ9k9dwGvNu4RN/1fIhYQrfJg6enJ5kEC5205OGJTuUKJiswGT20R3U38JtTuprpNgrauap3De0N5fpp9wbFZ8MXNzxC52VXSzBijn+E1XytOKDkwY8t8jbSiZiNRqm9QpeUtzpxay3QrhvwLX8WXC1PJC1ahgr+FAy0FKIBmrvZ6E1JpmW8/O8nWepwINn/6DYuEc0VhaYSrxhpMC4pEPxVC1dZAN1TwJXQP+OuUnnbwj1T4WP/5CpxV5lghYNauErqj7M/Al0xOnHL3d4WzWMyAtxQMrq6M3JDyfQz1clsNHR/t/+yUuAGYSFiuYWgjcvErcANBmKmpnQJdC2p67KnZPmWjEuCktUDfib7H93GJaIxVaIoECUajJqIuwo0Jp/1oTwkyl0YzAePcMM+iQWM1Ubq1cd+WBQE/Ccz9KBEIZMPLHjSRXeCtLT9j6FngqluB4ECOQPloKvoqWQEuKFk2tv8gbhk3QMsxdR0iRyI79DbotFVId+4hG/kv8JCC2dhPtNSnpjUDyS7h24gOMkOgHB6Zjj1n1rDRKagZEpynrtB/7qhK1mPJ6MgLlk9tN/y0biUsS3RmMob/ib7HwSFNcN4WSTB0p2tE9zDJYV1CTpsJd2JbqS05JJxid4UcA8ntSZJCFrQRUuVB8jUpWTPoKkdJJYg1AQ/GTFWs6rihpIJbJs/maBk+bNUENlouZqMALPRkJNdFQqLvijI1ZzPqO4Kx9XxsUAdcnRK9gyzukRwCjKzkleX/0CyfEtGj1XJeMgNrVc04m0y1ojGVFLblcBItDPxOQrym6i1Oc3j4xQBnmVJJOPOdCMlpd2k0ZxBOaNqaSOj2pHTaIpg4uI8yZqMGLML6YaSu0soE5RMD6RWMi7R6PHUh9lojIfgEpSbPXfS0s15GtsAliggVJBkzzCrSwSnoIT7ISh5dfkPJOtSMnqsSl5a1zTGcyYUU7kCZGpVyxSdUqFu7q4ZgjU+OW6YsGtgrDZS8qGbyrpUVShaukmg3azcMxSrLpXkYBy4h2gnI8bsQjqaZDqEZFyi0af22tlogBTlw0EJ7e23E91zg8ru+ORY+ab4dGkDskEXBKeghPuDkmF1+d9VMqN3N9pub0tMx3QzG1Lk3ixFigyAZGyFgru5k0jibkjuezOWTKiZ32Q0BOVwz1IneivsFrIbQgLjwziNV2n3lRbC1U3OCDuvowiR5T+QrPRIRo+xZL3mdzOH9nic94upBI9fLgbxugdLkZKrV34nQM+zb8qZSO044JIYS+bqUqWDiOTBPbo06P+GIIRd4Zq6jJ/dk07JNXIOmBuaoPHyH0jW48noMZbMlC1tpTzF1WSssV9MpQePOZBrX20VIqn7FnwnBpHCDZwZz+4YOqcTetigiEd4vEydtlJQmLpvxG/IWPK4XEYk63eeNulpoX5t3pxmIXvJjfF75RhCwdzhdvaZFtBnIIYo7X6jtQrd0lUVujenXf5TkpUMyWgYS1baLK1lLpVujNmvXOIuSUZa5wM5EaRFn0HxuvI1Z4pxpOTe5jMmaUH/rAfmMjUF0KyXqIIoXcopv3LF3oOxZKSV1TATl0zP7cs+tykUU3G+Eryi3uH5+IV6Cb3R00NWR1dludcK39D53/Bd0q0g+4PSavlPSVYyJOOSV5UXZMmqzow7CAL340ky1tivXLZwoCiPIZtTZDOvsU10Q0aUmdHSybeCXbc8S5J8+Lzn1rI/lWRodwhyhol7k4rAUqSsX/lWnkFpebDqbgwnYwfJdMgcdSdIq148QLmkLJapj4m2ajGYDMmUZ50P72E5lZKBvCez99xNd4Ntr9z5dJI69174oJLf8nSZIVL7v089KOyEhItSUr6lnhsVyuowckpUNXQmSk1n57EkH6JcGmPM8XG5NMaYEC6XxhgTwuXSGGNCuFwaY0wIl0tjjAnhcmmMMSFcLo0xJoTLpTHGhHC5NMaYEC6XxhgTwuXSGGNCuFwaY0wIl0tjjAnhcmmMMSFcLo0xJoTLpTHGBPjz53/7xlQ3WTVQlQAAAABJRU5ErkJggg==.
• C) data:image/png;base64,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.
• D) data:image/png;base64,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.

The standard five-point stencil in 2D PDEs updates a grid point based on:

• A) All points in the grid
• B) Only boundary points
• C) Only its diagonal neighbors
• D) Its four nearest neighbors along the horizontal and vertical directions

The subscript $(i,j)$ of $w$ in the grid (see Fig. below) in Finite Difference Scheme for the solution of a PDE, are_________ data:image/png;base64,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

• A) $(3,1)$
• B) $(1,3)$
• C) $(3,3)$
• D) $(1,1)$

A finite difference method when applied on PDE will be stable if the amplification factor G is ……

• A) Unbounded
• B) None of these
• C) Unrestrained
• D) Bounded

When solving the heat diffusion equation using Gauss–Seidel iteration, the interior temperature value​ is updated using:

• A) Only values from the previous iteration
• B) Only boundary values
• C) Randomly selected neighbor values
• D) A mix of updated values from iteration k+1 and old values from iteration k

The Crank-Nicolson scheme when applied on heat diffusion equation is ……

• A) Conditionally stable
• B) Neither stable nor bounded
• C) None of these
• D) Unconditionally stable