## 25 Reputation

10 years, 107 days

## how we make the code against that proble...

Maple

given differntial equations with boundary conditions.

f'''(x)+f(x)f''(x)+1-[f'(x)]^2+A*{1-f'(x)-(x/2)*f''(x)}=0,
g''(x)+P*[f(x)*g'(x)-f'(x)*g(x)-A*{g(x)+(x/2)*g'(x)}]=0,

bc's

f(0)=k,  f'(0)=m, g(0)=1,
f'(infinity)=1, g(infinity)=0

Dual solution exist in the given problem with shoot command i think. how we ll calculate them?

NOTE:

## how to plot f''(0), theta'(0) and phi'(0...

Maple 13

restart; b := 6; de1 := diff(f(eta), eta, eta, eta)+f(eta)*(diff(f(eta), eta, eta))-M^2*(diff(f(eta), eta))-(diff(f(eta), eta))^2 = 0, (1+(4/3)*Nr)*(diff(theta(eta), eta, eta))+epsilon*(theta(eta)*(diff(theta(eta), eta, eta))+epsilon*(diff(theta(eta), eta))^2)+Pr*(s*theta(eta)+f(eta)*(diff(theta(eta), eta))+Nb*(diff(theta(eta), eta))*(diff(phi(eta), eta))+Nt*(diff(theta(eta), eta))^2) = 0, diff(phi(eta), eta, eta)+Le*f(eta)*(diff(phi(eta), eta))+Nb*(diff(theta(eta), eta, eta...

## need help to calculate P1...

Maple 13

restart; with(Student[NumericalAnalysis]); with(PDEtools, casesplit, declare); x := .5; a := 1; b := .5; d := 1; Q := 2; omega := .4; h1 := 1+a*cos(x); h2 := -d-b*cos(x+omega); F := Q-1-d; de := diff(alpha*f(y), y, y, y, y)+G*(diff(theta(y), y, y))+B*(diff(phi(y), y, y))+6*beta*(diff(f(y), y, y))*(diff(f(y), y, y, y))^2+3*beta*(diff(f(y), y, y, y, y))*(diff(f(y), y, y))^2 = 0, diff(theta(y), y, y)+Nb*(diff(theta(y), y))*(diff(phi(y), y))+Nt*(diff(theta(y), y))^2 = 0, diff(phi(y...

## Error: Newton iteration is not convergin...

Maple

restart; b := 20; de1 := diff(f(eta), eta, eta, eta)+f(eta)*(diff(f(eta), eta, eta))+1-(diff(f(eta), eta))^2+k*(f(eta)^2*(diff(f(eta), eta))-2*f(eta)*(diff(f(eta), eta))*(diff(f(eta), eta, eta))) = 0, diff(theta(eta), eta, eta)+Pr*f(eta)*(diff(theta(eta), eta)) = 0, f(0) = 0, (D(f))(0) = 1, theta(0) = 1, (D(f))(b) = 0, theta(b) = 0; d1 := subs(Pr = .5, k = 1, [de1]); d2 := subs(Pr = 1, k = 1, [de1]); d3 := subs(Pr = 1.5, k = 1, [de1]); d4 := subs(Pr = 2, k = 1, [de1]); da1 := dsolve(d1, numeric...

## how to calculate dual solution problem...

Maple

restart;
b := 7; de1 := diff(f(eta), eta, eta, eta)-M^2*(diff(f(eta), eta))-(diff(f(eta), eta))^2+m1*f(eta)*(diff(f(eta), eta, eta)) = 0, diff(theta(eta), eta, eta)+m1*Pr*f(eta)*(diff(theta(eta), eta)) = 0, f(0) = S, (D(f))(0) = -1, (D(theta))(0) = -1, (D(f))(b) = 0, theta(b) = 0; d1 := subs(m1 = 1, S = 1.75, Pr = 0.7, M = 2, [de1]); d2 := subs(m1 = 1, S = 1.80, Pr = 0.7, M = 2, [de1]); d3 := subs(m1 = 1, S = 1.85, Pr = 0.7, M = 2, [de1]); d4 := subs(m1 = 1, S = 1.90, Pr = 0.7, M = 2, [de1...

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