Analytic/Numerical Solution of Elliptic PDE (Poisson Equation) with MATLAB

[@WonYYang]

%em07e01.m f=@(x,y)0; g=@(x,y)0; % Eq.(E7.1.1) w.r.t. Eq.(7.1.1) % (Rectangular) Domain and BC types x0=0; xf=pi; y0=0; yf=pi; D=[x0 xf y0 yf]; % BCs bx0=@(y)0; bxf=@(y)0; by0=@(x)sin(2*x); byf=@(x)0; % Eq.(E7.1.2a,b,c,d) % Numerical approach % Numbers of grid points along x-/y-axes, Error tolerance, Mx=50; My=50; tol=1e-5; MaxIter=600; [un,xx,yy]=pde_poisson_D(f,g,bx0,bxf,by0,byf,D,Mx,My,tol,MaxIter); % Analytical approach K=10; [ua,A]=pde_Laplace_ana(xf,yf,bx0,bxf,by0,byf,Mx,My,K); A, Discrepancy=norm(un-ua)/norm(ua) mesh(xx,yy,un) % Plot the solution graph xlabel('x'), ylabel('y') function [u,A,xx,yy]=pde_Laplace_ana(xf,yf,bx0,bxf,by0,byf,Mx,My,N) % To solve u_xx +u_yy = 0 % over the region D=[0,xf,0,yf]={(x,y)|0