Solving a system of equtions with first an pde and the others first order odes
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Now i have the same system but with the first equation be a PDE i would like to solve it pdepe solver and using ode45 1) R*dX/dt = -0.000038*X - (X*(X/Xinit)^frac)*rext -v*dX/dx + alpha*d^2X/dx^2 2) dY/dt = - 0.000038*Y + rext*X - rtra*Y + Sr. 3) dZ/dt = - 0.000038*Z + rext*Y - rtra*Z + Sti 4) dU/dt = 0.000038*U + rext*Z - rvol*U + Sfeu Satisfying Y(0)=Z(0)=U(0)=0 X(t,0)=0; dX/dx(t,x=L)=0; X(t=0,x)=Xinit Where the functions are X, Y,Z and U and the variables are x and t. The others parameters are known constant. If frac=0 i know how to.solve it with Laplace transform and then by an intégration over the space domaine i obtain X(t) and then the others functions (Y(t), Z(t), U(t)). Due toi the présence of frac i dont know how to solve it in MATLAB.