i. Common Software: Both explicit and implicit methods can be implemented in common software like MATLAB, Python, etc. However, the choice of method can depend on the specific software package being used. Some software may be better optimized for explicit methods, while others may be better for implicit methods.

ii. Stability: Explicit methods are conditionally stable, meaning they require certain conditions to be met for the solution to remain stable. On the other hand, implicit methods are unconditionally stable, meaning they remain stable regardless of the conditions.

iii. Computational Speed/Cost: Explicit methods generally have lower computational cost than implicit methods because they do not require the solution of simultaneous equations. However, the need for smaller time steps in explicit methods to ensure stability can increase the computational cost.

iv. Maximum Size of Computational Problem: Implicit methods can handle larger computational problems than explicit methods because they are not limited by stability conditions. However, the computational cost increases with the size of the problem.

v. Numerical Scheme: Explicit methods use information at the current time step to compute the solution at the next time step. Implicit methods, on the other hand, use information at the current and future time steps to compute the solution.

vi. Handling Nonlinearity: Implicit methods are generally better at handling nonlinearity than explicit methods. This is because implicit methods can handle larger time steps, which can be beneficial when dealing with nonlinear problems.

vii. Filtering of Frequencies: Explicit methods can cause numerical dispersion, which can distort the solution by introducing artificial frequencies. Implicit methods, on the other hand, have better frequency filtering capabilities and can provide more accurate solutions.

Question

i. Common Software: Both explicit and implicit methods can be implemented in common software like MATLAB, Python, etc. However, the choice of method can depend on the specific software package being used. Some software may be better optimized for explicit methods, while others may be better for implicit methods.

ii. Stability: Explicit methods are conditionally stable, meaning they require certain conditions to be met for the solution to remain stable. On the other hand, implicit methods are unconditionally stable, meaning they remain stable regardless of the conditions.

iii. Computational Speed/Cost: Explicit methods generally have lower computational cost than implicit methods because they do not require the solution of simultaneous equations. However, the need for smaller time steps in explicit methods to ensure stability can increase the computational cost.

iv. Maximum Size of Computational Problem: Implicit methods can handle larger computational problems than explicit methods because they are not limited by stability conditions. However, the computational cost increases with the size of the problem.

v. Numerical Scheme: Explicit methods use information at the current time step to compute the solution at the next time step. Implicit methods, on the other hand, use information at the current and future time steps to compute the solution.

vi. Handling Nonlinearity: Implicit methods are generally better at handling nonlinearity than explicit methods. This is because implicit methods can handle larger time steps, which can be beneficial when dealing with nonlinear problems.

vii. Filtering of Frequencies: Explicit methods can cause numerical dispersion, which can distort the solution by introducing artificial frequencies. Implicit methods, on the other hand, have better frequency filtering capabilities and can provide more accurate solutions.

Knowee AI · Accepted Answer

i. Common Software: Both explicit and implicit methods can be implemented in common software like MATLAB, Python, etc. However, the choice of method can depend on the specific software package being used. Some software may be better optimized for explicit methods, while others may be better for implicit methods.

ii. Stability: Explicit methods are conditionally stable, meaning they require certain conditions to be met for the solution to remain stable. On the other hand, implicit methods are unconditionally stable, meaning they remain stable regardless of the conditions.

iii. Computational Speed/Cost: Explicit methods generally have lower computational cost than implicit methods because they do not require the solution of simultaneous equations. However, the need for smaller time steps in explicit methods to ensure stability can increase the computational cost.

iv. Maximum Size of Computational Problem: Implicit methods can handle larger computational problems than explicit methods because they are not limited by stability conditions. However, the computational cost increases with the size of the problem.

v. Numerical Scheme: Explicit methods use information at the current time step to compute the solution at the next time step. Implicit methods, on the other hand, use information at the current and future time steps to compute the solution.

vi. Handling Nonlinearity: Implicit methods are generally better at handling nonlinearity than explicit methods. This is because implicit methods can handle larger time steps, which can be beneficial when dealing with nonlinear problems.

vii. Filtering of Frequencies: Explicit methods can cause numerical dispersion, which can distort the solution by introducing artificial frequencies. Implicit methods, on the other hand, have better frequency filtering capabilities and can provide more accurate solutions.

Write the comparison of Explicit and implicit method for following criteria: i. Common software ii. Stability iii. Computational speed/cost iv. Maximum size of computational problem v. Numerical scheme vi. Handling nonlinearity vii. Filtering of frequencies Question of CAE subject

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