www.gusucode.com > matlab 案例源码 matlab代码程序 > matlab/LaplacianOfMultivariateFunctionExample.m
%% Laplacian of Multivariate Function % Calculate and plot the discrete Laplacian of a multivariate function. %% % Define the x and y domain of the function. % Copyright 2015 The MathWorks, Inc. [x,y] = meshgrid(-5:0.25:5,-5:0.25:5); %% % Define the function $U(x,y) = \frac{1}{3} \left( x^4 + y^4 \right)$ over % this domain. U = 1/3.*(x.^4+y.^4); %% % Calculate the Laplacian of this function using |del2|. The spacing % between the points in |U| is equal in all directions, so you can specify % a single spacing input, |h|. h = 0.25; L = 4*del2(U,h); %% % Analytically, the Laplacian of this function is equal to $\Delta U(x,y) = % 4x^2 + 4y^2$. %% % Plot the discrete Laplacian, |L|. figure surf(x,y,L) grid on title('Plot of $\Delta U(x,y) = 4x^2+4y^2$','Interpreter','latex') xlabel('x') ylabel('y') zlabel('z') view(35,14) %% % The graph of |L| agrees with the analytic result for the Laplacian.