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Science Forum Index » Math - Numerical Analysis Forum » PDEtool Help
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| Guest |
 Posted: Mon Mar 26, 2007 5:34 am |
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first equation
∂n/∂t=0.003[(∂^2 n)/(∂x^2 )+(∂^2 n)/(∂y^2 )] - (∂[(0.38/(1+0.6c) n∂c)/
∂x┤+├ (0.38/(1+0.6c) n∂c)/∂y])/∂x- (∂[(0.38/(1+0.6c) n∂c)/∂x┤+├ (0.38/
(1+0.6c) n∂c)/∂y])/∂y – (0.28∂[n∂f/∂x+┤ n∂f/∂y])/∂x- (0.28∂[n∂f/∂x
+┤ n∂f/∂y])/∂y
second equation
∂c/∂t=-0.1n_i c
third equation
∂f/∂t=0.05n_i-0.1mf
fourth equation
∂m/∂t=〖e^(-6) n〗_i+0.01∇^2 m-0.3m
initial condition
n(0,x,y)=e^(-(-x^2)/(-0.001)) , 0≤x≤1
*c(0,x,y)={█(1,&0≤r≤0.1@〖((v-r)/(v-0.1)) 〗^2,&0.1≤r≤1)┤
Where
r^2=〖(x-1)〗^2+〖(y-0.5)〗^2
v=(√5-0.1)/(√5-1)
f(0,x,y)={(3〖e^〗^((-x^2)/0.45))/4} , 0≤x≤1
m(0.x.y)=0
I want to solve the above system numerically with PDEtool box. I want
to generate a new n at every time step = 0.01 that populates in a
10x10 matrix that is discretized to (0,1). However, i am not sure if
my system of equations are parabolic differential equations and my
initial and boundary conditions are Dirichlet (first kind). Can
someone guide me through this system with PDEtool box? any tips or
advices will be helpful. Thank you |
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