## 100 Reputation

3 years, 181 days

## How do I solve boundaty value problem wi...

Maple 18

eq1 := diff(f(x), x, x, x)+(1/2)*x*cos(alpha)*(diff(f(x), x, x))+(1/2)*sin(alpha)*f(x)*(diff(f(x), x, x))+G[r]*theta(x)+G[m]*phi(x) = 0;

eq2 := diff(theta(x), x, x)+(1/2)*Pr*cos(alpha)*x*(diff(theta(x), x))+sin(alpha)*f(x)*(diff(theta(x), x))+N[b]*(diff(theta(x), x))*(diff(phi(x), x))+N[t]*(diff(theta(x), x))^2 = 0;

eq3 := diff(phi(x), x, x)+(1/2)*Le*cos(alpha)*x*(diff(phi(x), x))+sin(alpha)*f(x)*(diff(phi(x), x))+N[t]*(diff(theta(x), x, x))/N[b] = 0;

ics := f(0) = 0, (D(f))(0) = gamma*((D@@2)(f))(0), theta(0) = 1+tau*(D(theta))(0), phi(0) = 1;

bcs := (D(f))(infty) = 0, theta(infty) = 0, phi(infty) = 0;

Parameters := G[r] = 5, G[m] = 3, Pr = 7, N[b] = .1, N[t] = .1, Le = 1, gamma = .2, tau = .1, alpha = 30*degree;

## How to simplify and substitute parameter...

Maple 18

I have a equation

((D@@2)(theta))(eta) = -(1/2)*(D(theta))(eta)*(-2*(D(phi))(eta)*beta*epsilon*lambda*D[B]+2*(D(phi))(eta)*beta*epsilon*mu*D[B]+f(eta)*sin(alpha)*beta*nu+2*(D(theta))(eta)*gamma*epsilon*D[t]-2*(D(theta))(eta)*beta*epsilon*D[t]+cos(alpha)*beta*eta*nu)/(beta*sigma)

and a parameters expression

Pr:=nu/sigma; N[b] := epsilon*D[B](mu-lambda)/sigma; N[t] := epsilon*D[t](gamma-beta)/(gamma*sigma); Le := nu/D[B]

How can I seperate common terms and substitute this parameters and got this following expression

((D@@2)(theta))(eta) = -(1/2)*Pr*(D(theta))(eta)*eta*cos(alpha)-(1/2)*Pr*(D(theta))(eta)*sin(alpha)*f(eta)-N[b]*(D(theta))(eta)*(D(phi))(eta)-N[t]*(D(theta))(eta)

## How to Convert PDE to ODE?...

Maple 18

How to conver a patial differetial equation to ordinary differential equation with or without dchange?

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## How to solve substitution?...

Maple

I have a PDE

eq1 := du/dx+dv/dy = 0; eq2 := du/dt+u*du/dx+v*du/dy-nu*d^2*u/dy^2 = 0

where u(x, y, t), v(x, y, t) and

eta(x, y, t):=y/((nu*t*cos(alpha)+(nu*x)/(U[w])*sin(alpha))^(1/(2)));

psi(x, y, t):=U[w]*(nu*t*cos(alpha)+(nu*x)/(U[w])*sin(alpha))^(1/(2))*f(eta(x,y,t));

u = diff(psi, y); v= -diff(psi, x).

How to substitiute u = diff(psi, y); v= -diff(psi, x) in eq1 and eq2, Also find the value of nu.

## How do I solve ODE system?...

Maple 18

How to solve ordinary differemtial equation system with initial conditions and boundary conditions. Here, some initial conditions are unknown variables. So how to find these  values of parameters.

eq1 := diff(f(x), x, x, x)+(1/2)*cos(alpha)*x*(diff(f(x), x, x))+(1/2)*sin(alpha)*f(x)*(diff(f(x), x, x)) = 0;

eq2 := diff(g(x), x, x)+diff(g(x), x)+(diff(g(x), x))*(diff(h(x), x))+cos(alpha)*x*(diff(g(x), x))+sin(alpha)*f(x)*g(x) = 0;

eq3 := diff(g(x), x, x)+diff(h(x), x, x)+1/2*(cos(alpha)*x+sin(alpha)*f(x)) = 0

ics:=f(0)=0, f'(0)=1, f''(0)=a[1], g(0)=1, g'(0)=a[2], h(0)=1, h'(0)=a[3];

bcs:=f(x) , g(x), h(x) tends to 0 ad x tends to infinity

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