## 60 Reputation

4 years, 215 days

## ODE with complex variable...

Maple

Dear Maplers

Consider the follwoing differential equation

```Deq:=(K*( Q*sinh(K)*cosh(Q)-K*cosh(K)*sinh(Q))*(1+s*K^2)
+p*(-4*K^2*Q*(K^2+Q^2)
+Q*(Q^4+2*K^2*Q^2+5*K^4)*cosh(K)*cosh(Q)
-K*(Q^4+6*K^2*Q^2+K^4)*sinh(K)*sinh(Q)));

pp := 0.077;
ss := 0;

ode:= diff(Q(K), K) = eval(subs(Q=Q(K),-(diff(Deq, K))/(diff(Deq, Q))),[p=pp,s=ss]);```

I aim to solve this DE numerically. Note that K and Q are complex variable and K varies from 0.1.e-5*I to 20.+1.e-5*I

`Q(0)=1e-10+1e-10*I`

I tried dsolve. but it does not get back correct solutions

```sol1 := dsolve({ode,Q(0)=1e-15+1e-15*I}, numeric, method=rkf45, output = listprocedure, abserr = 1.*10^(-6), relerr = 1.*10^(-6), range=0.0+1e-5*I .. 10.0+1e-5*I )
```

for example sol1(2.0+1e-5*I) return nothing

How can I solve this equation?

## all complex and real root of equation...

Maple

Dear Mapler

I want to find all real and complex solutions to the following equation. then calculate the omega based on these values and finally select the present the omega with the smallest imaginary part.

```with(SignalProcessing):

n:=8;

kk:=FFT(GenerateJaehne(n,1));

#params:= [p,    s, nu,   rho, h,    sigma, C1[1], C1[2], C2[1], C2[2], k1,  k2,  m1[1], m1[2], m2[1], m2[2] ]
params:= [1e-7, 0, 1e-6, 1e3, 1e-2, 0,     5e-4,  5e-4,  5e-4,  5e-4,  1.4, 1.4, 1+I,   1+I,   1-I,   1-I   ]:

for i from 1 to n do
x:=kk[i]:
mm[i]:=[solve(
eval(
( (x*h)*( (y*h)*sinh((x*h))*cosh((y*h))-(x*h)*cosh((x*h))*sinh((y*h)))*(1+s*(x*h)^2)
+p*(-4*(x*h)^2*(y*h)*((x*h)^2+(y*h)^2)+(y*h)*((y*h)^4+2*(x*h)^2*(y*h)^2+5*(x*h)^4)*cosh((x*h))*cosh((y*h))
-(x*h)*((y*h)^4+6*(x*h)^2*(y*h)^2+(x*h)^4)*sinh((x*h))*sinh((y*h))))
/((x*h)^2*(y*h)*cosh((y*h)))
, [p=params[1], s=params[2], h=params[5] ]), y
, AllSolutions=true)]:
print(kk[i]);
print(mm[i]);
for j from 1 to nops(mm[i]) do
omega[i][j]:=eval(-I*nu*((x*h)^2-mm[i][j]^2), [nu=params[3],h=params[5]]);
print(omega[i][j]);
od:
print(`======`);
od:
```

## coefficient of nonlinear terms...

Maple

Dear Mapler

I have an expression that consist of power of main variable x. I aim to fetch the coefficient of square root of x for example. I get an error when I am using COEFF(esp, sqrt(x))

Is there any solution?

## numerical solutions of PDE-integral equa...

Maple 2018

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

## recent posts removed...

Maple

Dear users

All my recent questions are removed by "mapleprimes" automatically. who knows the reason?

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