Question

USING MATLAB - Problem statement 24.7 Develop an M-file to implement the finite-difference approach for solving a linear second-order ODE with Dirichlet boundary conditions. Test it by duplicating Example 24.5. Example 24.5: Finite-Difference Approximation of Boundary Value Problems Problem Statement: Use the finite-difference approach to solve the same problem as in Examples 24.1 and 24.2. Use four interior nodes with a segment length of x = 2 m. Solution: Employing the parameters in Example 24.1 and x = 2 m, we can write Eq. (24.16) for each of the rod's interior nodes. For example, for node 1: T' + 2.2T = 40 Substituting the boundary condition T = 300 gives: 2.2T' - T = 340 After writing Eq. (24.16) for the other interior nodes, the equations can be represented as a tridiagonal and diagonally dominant matrix. MATLAB can be used to generate the solution: > A = [2.2 -1 0 0; -1 2.2 -1 0; 0 -1 2.2 -1; 0 0 -1 2.2] > b = [340; 40; 40; 40] > T = A\b The solution for T is approximately 83.2660.

Name: using matlab problem statement 247 develop an m file to implement the finite difference approach for solving a linear second order ode with dirichlet boundary conditions test it by duplicati 79971
Uploaded: 2023-07-26T03:26:58-08:00
Duration: 1 min 3 s
Channel: Numerade
Description: using matlab problem statement 247 develop an m file to implement the finite difference approach for solving a linear second order ode with dirichlet boundary conditions test it by duplicati 79971

          USING MATLAB - Problem statement

24.7 Develop an M-file to implement the finite-difference approach for solving a linear second-order ODE with Dirichlet boundary conditions. Test it by duplicating Example 24.5.

Example 24.5: Finite-Difference Approximation of Boundary Value Problems

Problem Statement: Use the finite-difference approach to solve the same problem as in Examples 24.1 and 24.2. Use four interior nodes with a segment length of x = 2 m.

Solution: Employing the parameters in Example 24.1 and x = 2 m, we can write Eq. (24.16) for each of the rod's interior nodes. For example, for node 1:

T' + 2.2T = 40

Substituting the boundary condition T = 300 gives:

2.2T' - T = 340

After writing Eq. (24.16) for the other interior nodes, the equations can be represented as a tridiagonal and diagonally dominant matrix. MATLAB can be used to generate the solution:

> A = [2.2 -1 0 0; -1 2.2 -1 0; 0 -1 2.2 -1; 0 0 -1 2.2]
> b = [340; 40; 40; 40]
> T = A\b

The solution for T is approximately 83.2660.

using matlab problem statement 247 develop an m file to implement the finite difference approach for solving a linear second order ode with dirichlet boundary conditions test it by duplicati 79971

Added by Melissa C.

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