# Question:How to solve the difference scheme solve and plot

## Question:How to solve the difference scheme solve and plot

Maple

Dear maple users,

i want to solve these 4 difference scheme equations to calculate the values of U,V,C,T and plot the graphs i verse U by fixing the values

i:=1,Sc:=2,Gr:=5,Gc:=10,DX:=0.02;DR:=0.2,Dt:=:=0.01:m:=7.44,7.88 where ,j=0..5;

eq1[i,j,m]:=(1/(4*DX))*(U[i, j-1,m+1]-U[i-1, j-1,m+1]+U[i,j,m+1]-U[i-1, j,m+1]- U[i-1, j-1,m]+U[i, j,m]-U[i-1, j,m])+(1/(2*DR))*(V[i, j,m+1]-V[i, j-1,m+1]+V[i, j,m]-V[i, j-1,m])+(1/(1+(j-1)*DR))*(V[i, j,m+1]):

eq2[i,j,m]:=(1/Dt)*(U[i, j,m+1]-U[i, j,m])+(U[i, j,m]/(2*DX))*(U[i, j,m+1]-U[i-1, j,m+1]+U[i, j,m]-U[i-1, j,m])+(V[i, j,m]/(4*DR))*(U[i, j+1,m+1]-U[i, j-1,m+1]+U[i, j+1,m]-U[i, j-1,m])=(Gr/2)*(T[i, j,m+1]+T[i, j,m])+(Gc/2)*(C[i, j,m+1]+C[i, j,m])+(1/(2*(DR)^2))*(U[i, j-1,m+1]-2*U[i, j,m+1]+U[i, j+1,m+1]+U[i, j-1,m]-2*U[i, j,m]+U[i, j+1,m])+(1/(4*DR*(1+(j-1)*DR)))*(U[i, j+1,m+1]-U[i, j-1,m+1]+U[i, j+1,m]-U[i, j-1,m]):

eq3[i,j,m]:=(1/Dt)*(T[i, j,m+1]-T[i, j,m])+(U[i, j,m]/(2*DX))*(T[i, j,m+1]-T[i-1, j,m+1]+T[i, j,m]-T[i-1, j,m])+(V[i, j,m]/(4*DR))*(T[i, j-1,m+1]-T[i, j-1,m+1]+T[i, j+1,m]-T[i, j-1,m])=(1/(2*Pr*(DR)^2))*(T[i, j-1,m+1]-2*T[i, j,m+1]+T[i, j+1,m+1]+T[i, j-1,m]-2*T[i, j,m]+T[i, j+1,m])+(1/(4*Pr*DR*(1+(j-1)*DR)))*(T[i, j+1,m+1]-T[i, j-1,m+1]+T[i, j+1,m]-T[i, j-1,m]):
eq4[i,j,m]:=(1/Dt)*(C[i, j,m+1]-C[i, j,m])+(U[i, j,m]/(2*DX))*(C[i, j,m+1]-C[i-1, j,m+1]+C[i, j,m]-C[i-1, j,m])+(V[i, j,m]/(4*DR))*(C[i, j+1,m+1]-C[i, j-1,m+1]+C[i, j+1,m]-C[i, j-1,m])=(1/(2*Sc*(DR)^2))*(C[i, j-1,m+1]-2*C[i, j,m+1]+C[i, j+1,m+1]+C[i, j-1,m]-2*C[i, j,m]+C[i, j+1,m])+(1/(4*Sc*DR*(1+(j-1)*DR)))*(C[i, j+1,m+1]-C[i, j-1,m+1]+C[i, j+1,m]-C[i, j-1,m]):

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