51 lines
1.1 KiB
Mathematica
51 lines
1.1 KiB
Mathematica
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function [x,t,c] = UW_scheme(xf,N,T,K,U,c0)
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% ---- Numerical solution of the linear advection equation in a periodic domain ----
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% c_t+ U * c_x = 0 with domain [0,xf]
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% given the initial condition c0.
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% -----------------------------------------------
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% Sintax:
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% [x,t,c] = UW_scheme(xf,N,T,K,U,c0)
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%
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% Input:
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% xf end of our domain
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% N number of space intervals
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% T max time
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% K number of time intervals
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% U convection velocity
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% c0 initial condition
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%
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% Output:
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% x vector of spatial nodes
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% t vector of time nodes
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% c numerical solution
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% Space and time intervals size
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dx=xf/N;
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dt=T/K;
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% initialization of x and t vectors (nodes)
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x=linspace(0,xf,N+1)';
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t=linspace(0,T,K+1)';
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% Solution matrix
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c=zeros(N+1,K+1);
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% Initial conditions
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c(:,1) = c0(x);
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% Creating our matrix
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e = ones(N+1,1);
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B = spdiags([-e,e],[-1,0],N+1,N+1);
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I = speye(N+1);
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%"printing" courant number and numerical viscosity
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C0=(U*dt/dx)
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numerical_viscosity= U*dx*(1-C0)/2
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%final metrix to compute the solution
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A = I - C0*B;
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%finding the solution
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for k=1:K
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c(1:end,k+1) = A*c(1:end,k);
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end
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