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Question: numerical solutions of PDE-integral equation

Question:numerical solutions of PDE-integral equation

arashghgood 60 Maple 2018
homework pde pdsolve differential-equations integro-differential-equation
April 25 2020
0

Dear experts

I am interested to solve the following equation numerically by Maple. I would appreciate it if you let me how I can do and what the boundary conditions and initial values are needed


eq:= diff(2*diff(eta(x,y,t),t)+3*eta(x,y,t)*diff(eta(x,y,t),x)+(1/3-1/epsilon/B)*diff(eta(x,y,t),x,x,x),x)+diff(eta(x,y,t),y,y)-1/sqrt(Pi*R)*int(diff(eta(x+zeta,y,t),x,x)/sqrt(zeta),zeta=0..t/epsilon)=0;
where

1) epsilon, B and r are constant

2) 1/epsilon/B is not equal to 1/3 at all
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