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Gauss-Siedel Matrix to solve Elliptic Equation
Qs: Write a FORTRAN program to approximately solve elliptic equation : - u_xx - u_yy=1 with the five-point finite difference formula in the right-angled triangle, sides 1,2,3^(1/2) using the Gauss-Seidel matrix solver withe the boundary conditions u=0 on all sides. Take a mesh spacing to be... -
Jacobi iterative method to solve elliptic equation
Qs: Write a FORTRAN program to approximately solve elliptic equation :-u_xx-u_yy=1 on a unit square -1<x<1, -1<y<1, with u=0 on the entire boundary. Use the five -point finite difference formula on a uniform mesh of size h in each direction. Set up the matrix system Au=b (taking the natural... -
CRANK-NICOLSON SCHEME TO SOLVE HEAT DFFUSION EQUATIONI
QUESTION: Heat diffusion equation is u_t= (D(u)u_x)_x. Modify this program to investigate the following developments: Allow for the diffusivity D(u) to change discontinuously, with initial data as u(x,0)= (1+x)(1-x)^2. boundary values u(+-1,t)=0. Treat in detail the case D(u)=1 when x<1/2 and... -
heat equation using crank-nicolsan scheme in fortran
Program crank_nicolson call thomas(a,b,c,d,JI) Real, allocatable :: x(:),u(:),a(:),b(:),c(:),d(:) Real:: m,dx,dt,Tmax Integer:: j,NI,JI Print*, 'Enter the total number of time steps' read*, NI Print*, 'Enter the final time' read*, Tmax dt=Tmax/NI !The size of timestep Print*, 'This gives...
