Find the solution of the initial boundary value problem , &nbs

Question

Find the solution of the initial boundary value problem , $\frac{\partial ^2u}{\partial ^2} = \frac{\partial ^2u}{\partial x^2},0 \leq x \leq1$

$u(x,0) = sin\pi x,0\leq x\leq 1 \frac{\partial u}{\partial t}(x,0)=0, u(0,t)=u(l,t)=0,t>0$

by using second order explicit method with . $h=\frac{1}{4},r=\frac{1}{3}$ Integrate for one time step.

22 Mar 2023

Answer :

Word Count : 327

To solve the initial boundary value problem using the second-order explicit method, we first need to discretize the spatial and temporal domains. Let N be the number of grid points in the x-direction and M be the number of time steps. We can define the grid spacing in the x-direction as h = 1/N and the time step as k = r*h^2, where r is a constant that determines the stability of the numerical scheme.

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