Develop a MATLAB code to solve the FTCS 2D heat diffusion equation -AV f in a...

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Develop a MATLAB code to solve the FTCS 2D heat diffusion equation -AV² f in a domain (x,y)= (0,1)x(0,1) with initial condition: f(x,y,0)= x(1-x)y(1-y)= f(x,y) and boundary conditions: f(x,0,t)= f(x,l,t) = f(0, y,t)=f(1,y,t)=0. at Use the following parameters: x=0.1; Ay= Ax=0.05; At=(Ax² /x)/4;1=20At Generate a solution and compare to the series analytical solution 120-n'r [-1]+12nn-1] +24+24 [1])(-2+2[-]"). N (x,y)= Σ Σ series n'x¹m² n-1m-1 series (a) Show a surface plot of fari. (x,y,0)-f(x,y) (this quantity should be (10) Question: Why do this test? (b) In a second surfate plot shown fres(X,Y,tat) (c) In a third surface plot show Frics (X,Ust float)-Series (X,Y,t final) FICS (d) Report L_ norm for the error. This number should be (10) CIN =100]: Lxsin(nxx)sin(mzy)e series Develop a MATLAB code to solve the FTCS 2D heat diffusion equation -AV² f in a domain (x,y)= (0,1)x(0,1) with initial condition: f(x,y,0)= x(1-x)y(1-y)= f(x,y) and boundary conditions: f(x,0,t)= f(x,l,t) = f(0, y,t)=f(1,y,t)=0. at Use the following parameters: x=0.1; Ay= Ax=0.05; At=(Ax² /x)/4;1=20At Generate a solution and compare to the series analytical solution 120-n'r [-1]+12nn-1] +24+24 [1])(-2+2[-]"). N (x,y)= Σ Σ series n'x¹m² n-1m-1 series (a) Show a surface plot of fari. (x,y,0)-f(x,y) (this quantity should be (10) Question: Why do this test? (b) In a second surfate plot shown fres(X,Y,tat) (c) In a third surface plot show Frics (X,Ust float)-Series (X,Y,t final) FICS (d) Report L_ norm for the error. This number should be (10) CIN =100]: Lxsin(nxx)sin(mzy)e series

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To solve the 2D heat diffusion equation using the Forward Time Centered Space FTCS method in MATLAB ... View the full answer