Saha

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Could you Please Help me,the Maple code for Plot this equations in any Numerical Method

restart

with(PDETools, declare):

with(LinearAlgebra):

with(PolynomialIdeals):

with(plots):

declare(f(x));

f(x)*`will now be displayed as`*f

(1)

eq1 := diff(f(x), x, x, x)+(1/2)*(1-phi)^2.5*(1-phi+phi*rho[s]/rho[fl])*(eta*`cosω`+f(x)*`sinω`)*(diff(f(x), x, x))+(1-phi)^2.5*M*sin^2*alpha*(1-(diff(f(x), x)))+(1-phi)^2.5*(1-phi+phi*`ρβ`[s]/`ρβ`[fl])*lambda[T]*theta = 0;

diff(diff(diff(f(x), x), x), x)+(1/2)*(1-phi)^2.5*(1-phi+phi*rho[s]/rho[fl])*(eta*`cosω`+f(x)*`sinω`)*(diff(diff(f(x), x), x))+(1-phi)^2.5*M*sin^2*alpha*(1-(diff(f(x), x)))+(1-phi)^2.5*(1-phi+phi*`ρβ`[s]/`ρβ`[fl])*lambda[T]*theta = 0

(2)

eq2 := K[nf]*(diff(theta(x), x, x))/K[f]+(1/2)*Pr*(eta*`cosω`+f*`sinω`)*(diff(theta(x), x)) = 0;

K[nf]*(diff(diff(theta(x), x), x))/K[f]+(1/2)*Pr*(eta*`cosω`+f*`sinω`)*(diff(theta(x), x)) = 0

(3)

bcs := F(0) = 0, F(1) = 0, F(10) = 1, Theta(0) = 1, Theta(10) = 0;

F(0) = 0, F(1) = 0, F(10) = 1, Theta(0) = 1, Theta(10) = 0

(4)

a1 := [M = 1, alpha = 0, phi = 0.5e-1, `cosω` = 1, `sinω` = 1, sin(alpha) = 0, lambda[T] = 0, Pr = 6.2, rho[s] = 5200, rho[fl] = 997.1, `ρβ`[fl] = 20939.1, K[nf] = .6842, eta = 0];

[M = 1, alpha = 0, phi = 0.5e-1, `cosω` = 1, `sinω` = 1, sin(alpha) = 0, lambda[T] = 0, Pr = 6.2, rho[s] = 5200, rho[fl] = 997.1, `ρβ`[fl] = 20939.1, K[nf] = .6842, eta = 0]

 

[Pr = 6.2, M = 1, phi = 0.5e-1, `cosω` = 1, `sinω` = 1, sin(alpha) = 0, lambda[T] = 0, `ρβ`[fl] = 20939.1, K[nf] = .6842, K[f] = .613, eta = 0]

(5)

b1 := subs(a1, eq1);

diff(diff(diff(f(x), x), x), x)+.5325197465*f(x)*(diff(diff(f(x), x), x)) = 0

(6)

c1 := subs(a2, eq2);

1.116150082*(diff(diff(theta(x), x), x))+3.100000000*f*(diff(theta(x), x)) = 0

(7)

d1 := dsolve({b1, bcs}, {bcs, c1}, numeric); d1(0)

Error, (in dsolve/numeric/process_input) invalid argument: {1.116150082*(diff(diff(theta(x), x), x))+3.100000000*f*(diff(theta(x), x)) = 0, F(0) = 0, F(1) = 0, F(10) = 1, Theta(0) = 1, Theta(10) = 0}

 

d1(0)

(8)

``

Download  Numerical Method.mw


How to find the values of X(1),X(2),..&Y(1),Y(2)...Plese help .

restart;

 

for k from 0 to 5 do
X(k+1):=solve(2*(k+1)*X(k+1)+(k+1)*Y(k+1)-X(k)-Y(k)+(1)/k!,X(k+1));
Y(k+1):=solve((k+1)*X(k+1)+(k+1)*Y(k+1)+2*X(k)+Y(k)+(1)/k!,Y(k+1)); od;


 

2

 

1

 

Warning, solving for expressions other than names or functions is not recommended.

 

Error, (in solve) a constant is invalid as a variable, -(1/2)*Y(1)+1

 

``

Download DE_Using_DTM-Ex-3(1).mw

 


could you please help me ,the maple code for this given series.

restart

U[0](x) := x;

x

(1)

"U[k+1](x):=solve((k+1)*U[k+1](x)+(x*(-1)^((k-1)/(2)))/(k!)-x^(2)*((e)^(x))/(10){6/(k!)-sum((2^(k[1]))/(k[1!])(5*delta[k[]-k[1]](x)+(2^(k-k[1])*(-1)^((k-k[1])/(2)))/((k-k[1])!)+(2^(k-k[1]+1)*(-1)^((k-k[1]-1)/(2)))/((k-k[1])!)),k[1]=0..k)}-(cos^(2)(x)+sin^()(x))*((∂)^2)/((∂)^( )x^2) [U[k](x)]-(e)^(x)[sum(1/(k[1]!){1/(k-k[1])(sum(sum(1/(k[3]!)*U[k[2]-k[3]](x)*U[k-k[1]-k[2]-1](x)},k[1]=0..k),k[2]=0..k-k[1]-1),k[3]=0..k[2])),U[k+1](x)];  od;"

Error, unable to match delimiters

"U[k+1](x):=solve((k+1)*U[k+1](x)+(x*(-1)^((k-1)/2))/(k!)-x^2*((e)^x)/10{6/(k!)-sum((2^(k[1]))/(k[1!])(5*delta[k-k[1]](x)+(2^(k-k[1])*(-1)^((k-k[1])/2))/((k-k[1])!)+(2^(k-k[1]+1)*(-1)^((k-k[1]-1)/2))/((k-k[1])!)),k[1]=0..k)}-(cos^2(x)+sin(x))*((∂)^2)/(∂x^2) [U[k](x)]-(e)^x[sum(1/(k[1]!){1/(k-k[1])(sum(sum(1/(k[3]!)*U[k[2]-k[3]](x)*U[k-k[1]-k[2]-1](x)},k[1]=0..k),k[2]=0..k-k[1]-1),k[3]=0..k[2])),U[k+1](x)];  od;"

 

``


 

Download Chapter_6-Example-6.5.4.mw

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