How to Solve this “First-order wave equation” using Euler’s time-stepping series to obtain a graph similar to above. Solve this using Runga Kutta time-stepping series also.

11 views (last 30 days)
% This program describes a moving 1-D wave
% using the finite difference method
clc
close all;
%%
% Initialization
Nx= 480; % x-Grid
dx= 3/480; % Step size
x(:,1)= (0:Nx-1)*dx;
f= 125.7; % Wave number
U(:,1)= -16*(x(:,1)-1/2).^2
% U(:,1) = exp(-16*(x(:,1)-1/2).^2);
U(:,1)= exp(U(:,1));
U(:,1)= U(:,1).*sin(f*x(:,1))
%U(:,1)= exp(-16*(x(:,1)-1/2).^2)%sin*(f*x(:,1))
%U(:,1)= U(:,1).*sin(f*x(:,1))
mpx= (Nx+1)/2; % Mid point of x-axis
% (Mid point of 1 to 3= 2 here)
T= 10; % Total no. of time step
f= 125.7; % Wave number
dt= 0.000625; % time-step
t(:,1)= (0:T-1)*dt;
v= 1; % wave velocity
c=v*(dt/dx); % CFL condition
s1= floor(T/f);
%%
% Initial condition
x=0:.001:3;
u=@(t)exp(-16*(x-(.75*t+.5)).^2).*sin(125.7*x);
plot(x,u(0))
figure
plot(x,u(2))

Answers (0)

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by