How to solve these pde equations in maple to get the similar type graphs.

Ode equations we can solve directly but these equations are pde .

in the article they have solved the governing equations by series solution? 

can we solve these equations in maple also by series solution or any other method is there to solve these equations

Dear sir,

In the given problem, eta = 0 to 20, I want the table value of eta for a step size of 1000 (0 to 20 in thousand parts).

i have calculated only for one value, zero

Download Demo_paper_work.mw

I want like this plots here two phase are there boundary is -2 to0 and 0 to 2

f(±2)=0,g(±2)=0,f(0)=1,h(±2)=1,H(±2)=1

How to integrate the below term

int((n*p+exp(n*p))*exp(-p)*p^(s-1)*f^s/((n*p+exp(2*n*p))*factorial(s)), p = 0 .. 1);
eval(%);

det_roots.docx

How to find the roots of the equation ?

like if the roots of the equations are m ,n,o,p then the value of these roots in terms of λ₀  λ₁  λ₂  λ₃  µ1  µ2 and  µ3