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Hello all..

Im sharena and i am solving ODE BVP by using maple. i used this command to solved the equation..

 

However, i dont know which method this programm solved my ODE. Is it RK45 method??

restart;
Digits := 5;
with(ODETools);
with(student);
with(plots);
inf := 5;
with(LinearAlgebra);
equ1 := (1+2*n)*f(eta)*(diff(theta(eta), eta))/(1+3*n)-(diff(theta(eta), `$`(eta, 2))) = 0;
equ2 := ((1+n)*(diff(f(eta), eta))^2/(1+3*n)-(1+2*n)*f(eta)*(diff(f(eta), eta, eta))/(1+3*n))/Bo+(diff(f(eta), `$`(eta, 3)))^n-theta(eta) = 0;
Bcs := f(0) = 0, (D(f))(0) = 0, (D(f))(inf) = 0, theta(0) = 1, theta(inf) = 0;
Bo := 1; n := 2;
SolP1 := dsolve({Bcs, equ1, equ2}, numeric);
Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system
SolP1(0);
SolP1(0)

> restart:with(plots):blt:=7:

 

 

> lambda:=2:m:=3:s:=1:

> Eq1:=(diff(f(eta),eta,eta,eta))+(f(eta)*(diff(f(eta),eta,eta)))-((diff(f(eta),eta))^2)+lambda*(((f(eta)*(diff(f(eta),eta,eta,eta))))-2*(diff(f(eta),eta))*(diff(f(eta),eta,eta,eta))^2)-(M/(1+m^2))*((diff(f(eta),eta)+ms))=0;

 

>

> Eq2:=(diff(h(eta),eta,eta))+(f(eta)*(diff(h(eta),eta)))-((diff(f(eta),eta))*(h(eta)))+lambda*(((f(eta)*(diff(h(eta),eta,eta,eta))))+(h(eta)*(diff(f(eta),eta,eta,eta)))+(diff(f(eta),eta,eta))*(diff(h(eta),eta))-2*(diff(f(eta),eta))*(diff(h(eta),eta,eta))+(M/(1+m^2)))*(m*(diff(f(eta),eta)-h))=0;

 

>

> Eq3:=((f(eta))*(diff(theta(eta),eta)))+Pr*((diff(theta(eta),eta,eta)))=0;

 

>

> bcs1 := f(0) = 0, (D(f))(0) = 1, (h)(0) = 0, (theta)(0) = 1, (D(f))(blt) = 0,  h(blt) = 0, theta(blt) = 0, D(D(f))(blt) = 0, (D(h))(blt)=0;

 

>

> L := [1,2,3];

 

> for k to 3 do R := dsolve(eval({Eq1, Eq2, Eq3, bcs1}, M = L[k]), [f(eta),h(eta),theta(eta)], numeric, maxmesh=10000, output = listprocedure);;Y || k := rhs(R[3]); YA || k := rhs(R[6]);YB || k := rhs(R[5]);YC || k := rhs(R[4]);YD || k := rhs(R[7]);end do:

>

 

>

>

Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system

hi

please help me for dsolve differential equations...after much time dont answer!!!

thanks..

dsolve.mw

Digits := 15; SYS := [.16783*h1(theta)-0.96238e-3*(diff(h1(theta), theta, theta))+0.61603e-1*(diff(h2(theta), theta))+0.14870e-4*(diff(h2(theta), theta, theta, theta))-.23703*h3(theta)-0.84431e-3*(diff(h3(theta), theta, theta))+3.4919*10^(-7)*(diff(h1(theta), theta, theta, theta, theta)) = 0, 2.3940*h2(theta)-.35329*(diff(h2(theta), theta, theta))-0.68260e-1*(diff(h1(theta), theta))-0.16526e-4*(diff(h1(theta), theta, theta, theta))+3.0808*(diff(h3(theta), theta))-0.17833e-2*(diff(h3(theta), theta, theta, theta)) = 0, 9.4813*10^(-7)/((1.+1.5802*10^(-8)*h3(theta))*ln(10.+1.5802*10^(-7)*h3(theta))^2)-3.1867/((1.-0.26556e-1*h3(theta))*ln(10.-.26556*h3(theta))^2)-7.6530/((1.-0.31888e-1*h3(theta))*ln(10.-.31888*h3(theta))^2)-4.2551/((1.-0.35459e-1*h3(theta))*ln(10.-.35459*h3(theta))^2)-9.0315/((1.-0.37632e-1*h3(theta))*ln(10.-.37632*h3(theta))^2)-4.6587/((1.-0.38822e-1*h3(theta))*ln(10.-.38822*h3(theta))^2)-9.4520/((1.-0.39384e-1*h3(theta))*ln(10.-.39384*h3(theta))^2)+0.74999e-1/((1.+0.12500e-2*h3(theta))*ln(10.+0.12500e-1*h3(theta))^2)-.69143/((1.-0.28810e-2*h3(theta))*ln(10.-0.28810e-1*h3(theta))^2)-.12945/(1.-0.38836e-1*h3(theta))^4-0.38260e-1/(1.-0.11478e-1*h3(theta))^4-0.24826e-1/(1.-0.37240e-2*h3(theta))^4+0.74712e-3*(diff(h3(theta), theta, theta, theta, theta))+2.6337*10^(-8)/(1.+1.5802*10^(-8)*h3(theta))^4-0.27242e-1*(diff(h3(theta), theta, theta))-3.0707*(diff(h2(theta), theta))+0.17833e-2*(diff(h2(theta), theta, theta, theta))-.23618*h1(theta)-0.84126e-3*(diff(h1(theta), theta, theta))-0.89222e-1/(1.-0.26767e-1*h3(theta))^4-.21340/(1.-0.32010e-1*h3(theta))^4-.13154/(1.-0.19732e-1*h3(theta))^4-0.88519e-1/(1.-0.26556e-1*h3(theta))^4-4.7454/((1.-0.39545e-1*h3(theta))*ln(10.-.39545*h3(theta))^2)-0.36390e-1/(1.-0.10917e-1*h3(theta))^4-1.3100/((1.-0.10917e-1*h3(theta))*ln(10.-.10917*h3(theta))^2)-.89374/((1.-0.37240e-2*h3(theta))*ln(10.-0.37240e-1*h3(theta))^2)-1.3773/((1.-0.11478e-1*h3(theta))*ln(10.-.11478*h3(theta))^2)-.11820/(1.-0.35459e-1*h3(theta))^4-.26259/(1.-0.39388e-1*h3(theta))^4-4.7356/((1.-0.19732e-1*h3(theta))*ln(10.-.19732*h3(theta))^2)+28.586*h3(theta)-.21258/(1.-0.31888e-1*h3(theta))^4-9.4531/((1.-0.39388e-1*h3(theta))*ln(10.-.39388*h3(theta))^2)-4.6603/((1.-0.38836e-1*h3(theta))*ln(10.-.38836*h3(theta))^2)-9.0393/((1.-0.37664e-1*h3(theta))*ln(10.-.37664*h3(theta))^2)-4.2631/((1.-0.35526e-1*h3(theta))*ln(10.-.35526*h3(theta))^2)-7.6824/((1.-0.32010e-1*h3(theta))*ln(10.-.32010*h3(theta))^2)-.25088/(1.-0.37632e-1*h3(theta))^4-.12919/(1.-0.19378e-1*h3(theta))^4-.11842/(1.-0.35526e-1*h3(theta))^4-.12941/(1.-0.38822e-1*h3(theta))^4+0.20833e-2/(1.+0.12500e-2*h3(theta))^4-0.19206e-1/(1.-0.28810e-2*h3(theta))^4-4.6507/((1.-0.19378e-1*h3(theta))*ln(10.-.19378*h3(theta))^2)-.26255/(1.-0.39384e-1*h3(theta))^4-.13182/(1.-0.39545e-1*h3(theta))^4-.25109/(1.-0.37664e-1*h3(theta))^4-3.2120/((1.-0.26767e-1*h3(theta))*ln(10.-.26767*h3(theta))^2) = 0]

ode2 := diff(SYS[2], theta); SYS2 := {ode2, SYS[1], SYS[3]}; bcs2 := {h1(0) = 0, h1(1) = 0, h2(0) = 0, h2(1) = 0, h3(0) = 0, h3(1) = 0, ((D@@1)(h1))(0) = 0, ((D@@1)(h1))(1) = 0, ((D@@1)(h3))(0) = 0, ((D@@1)(h3))(1) = 0}; bcs22 := eval[recurse](convert(SYS[2], D), `union`({theta = 1}, bcs2)); res2 := dsolve(`union`(`union`(SYS2, bcs2), {bcs22}), 'maxmesh' = 2024, numeric, method = bvp[middefer], range = 0 .. 1, abserr = 0.1e-3, output = listprocedure)

NULL



Download dsolve.mw

 


Hello Dr/Prof?sir?madam

i have problem on running the ode bcs

there is cos n sine in ther ode

any idea to solve this ?

i have attched it

thnks
Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/Sc.mw .

Download Sc.mw

How can i over come convergence error, i am unable to apply approxsoln appropriately and continouation as well. regards

N := 5;

-(1/2)*Pr*n*x*(diff(f(x), x))*(diff(theta(x), x))-(1/2)*Pr*(n+1)*f(x)*(diff(theta(x), x))-(1/2)*(n+1)*(diff(diff(theta(x), x), x))+Pr*gamma*((1/4)*(n^2-3*n+3)*x^2*(diff(f(x), x))*(diff(diff(f(x), x), x))*(diff(theta(x), x))+(1/4)*(2*n^2+5*n+3)*f(x)*(diff(f(x), x))*(diff(theta(x), x))+(1/4)*n(n+1)*x*f(x)*(diff(diff(f(x), x), x))*(diff(theta(x), x))+(1/4)*(2*n^2+3*n-3)*x*(diff(f(x), x))^2*(diff(theta(x), x))+(1/4)*(n-1)*x^2*(diff(diff(f(x), x), x))*(diff(theta(x), x))+(1/2)*n*(n+1)*x*f(x)*(diff(f(x), x))*(diff(diff(theta(x), x), x))+(1/4)*(n^2-1)*(diff(f(x), x))^2*(diff(theta(x), x))+(1/4)*(n+1)^2*f(x)^2*(diff(diff(theta(x), x), x))+(1/4)*(n-1)^2*x^2*(diff(f(x), x))^2*(diff(diff(theta(x), x), x))) = 0

(1)

bc := (D(theta))(0) = -Bi*(1-theta(0)), theta(N) = 0, f(0) = 0, (D(f))(0) = 0, (D(f))(N) = 1;

(D(theta))(0) = -Bi*(1-theta(0)), theta(5) = 0, f(0) = 0, (D(f))(0) = 0, (D(f))(5) = 1

(2)

a1 := dsolve(subs(beta = .1, n = .5, Pr = 10, gamma = .1, Bi = 50, {bc, eq1, eq2}), numeric, method = bvp[midrich], abserr = 10^(-8), output = array([seq(.1*i, i = 0 .. 10*N)]))

Error, (in dsolve/numeric/BVPSolve) initial Newton iteration is not converging

 

``

 

Download ehtasham.mwehtasham.mw

Hi,
I want to plot stream lines from a stream function given by " psi = x*f(eta)+int(h(s), s = 0 .. eta) " where "f(eta)" and "h(eta)" are the solution of the differential equation given below:

restart;
with(linalg);
Digits := 24;

eq1:=diff(f(eta),eta,eta,eta)+f(eta)*diff(f(eta),eta,eta)-(diff(f(eta),eta))^2+1;
eq2 := diff(h(eta),eta,eta)+f(eta)*diff(h(eta),eta)-diff(f(eta),eta)*h(eta);
bc:=f(0)=0,D(f)(0)=0,D(f)(6)=1,h(0)=0,D(h)(6)=1;
A1:=dsolve({eq1,eq2,bc},numeric,method=bvp[midrich],abserr = 1.*10^(-10),output=operator):

How can I do this?

I want to solve system of non linear odes numerically.

I encounter following error

Error, (in dsolve/numeric/bvp) cannot determine a suitable initial profile, please specify an approximate initial solution

how to correct it

regards

i want to solve these two coupled eqaut with finite boundary conditionsions. Can some one help me

eq1:=diff(f(eta),eta,eta,eta,eta)+2*(epsilon/(1+epsilon*theta(eta)))^2*diff(f(eta),eta,eta)*((diff(theta(eta),eta))^2)-(epsilon/(1+epsilon*theta(eta)))*(diff(theta(eta),eta,eta))*(diff(f(eta),eta,eta))=0;

eq2:=diff(theta(eta),eta,eta)+Pr*Re*f(eta)*diff(theta(eta),eta)=0;

Re:=1:Pr:=1:epsilon:=0.25:

bc:=f(1)=0,D(f)(-1)=0,D(f)(1)=1,D(f)(-1)=1,theta(-1)=0,theta(1)=0;

 

Hi,

 

I want to solve the Falkner-Skan equation numbercally using maple. The Falkner-Skan equation is 

f′′′ + ff′′ + (1 − (f′)^2)=0 ,

with subject to the boundary conditions,

f(0) =0 ; f′(0) = 0,

f′(∞) = 1. 

could you  please help me to have loop to solve this problem from t=0..30.

And then save the data in DATfile in order to plot using Gnuplot?

 

Regards

 

Hai everyone

may i ask why solution have an error?

hope i have an answer

r

 

NULL

restart

with(plots):

Pr := 6.8:

Eq1 := (101-100*lambda)*(diff(f(eta), `$`(eta, 3)))+f(eta)*(diff(f(eta), `$`(eta, 2)))+2*delta*theta(eta)+2*delta*Nc*gamma(eta)-2*delta*Nr*phi(eta);

(101-100*lambda)*(diff(diff(diff(f(eta), eta), eta), eta))+f(eta)*(diff(diff(f(eta), eta), eta))+2*theta(eta)+2*gamma(eta)-2*phi(eta)

(1)

Eq2 := (101-100*lambda)*(diff(theta(eta), `$`(eta, 2)))+Pr*f(eta)*(diff(theta(eta), eta))+Pr*Nb*(diff(theta(eta), eta))*(diff(phi(eta), eta))+Pr*Nt*(diff(theta(eta), eta))^2;

(101-100*lambda)*(diff(diff(theta(eta), eta), eta))+6.8*f(eta)*(diff(theta(eta), eta))+3.40*(diff(theta(eta), eta))*(diff(phi(eta), eta))+3.40*(diff(theta(eta), eta))^2

(2)

Eq3 := (101-100*lambda)*(diff(phi(eta), `$`(eta, 2)))+Le*f(eta)*(diff(phi(eta), eta))+Nt*(diff(theta(eta), `$`(eta, 2)))/Nb;

(101-100*lambda)*(diff(diff(phi(eta), eta), eta))+.1*f(eta)*(diff(phi(eta), eta))+1.000000000*(diff(diff(theta(eta), eta), eta))

(3)

Eq4 := (101-100*lambda)*(diff(gamma(eta), `$`(eta, 2)))+Sc*s*(diff(theta(eta), `$`(eta, 2)))+Sc*f(eta)*(diff(gamma(eta), eta));

(101-100*lambda)*(diff(diff(gamma(eta), eta), eta))+.30*(diff(diff(theta(eta), eta), eta))+.6*f(eta)*(diff(gamma(eta), eta))

(4)

VBi := [10, 20, 30]:

etainf := 5:

bcs := f(0) = 0, (D(f))(0) = 0, (D(theta))(0) = -Bi*(1-theta(0)), phi(0) = 1, gamma(0) = 1, (D(f))(etainf) = 1, theta(etainf) = 0, phi(etainf) = 0, gamma(etainf) = 0;

f(0) = 0, (D(f))(0) = 0, (D(theta))(0) = -Bi*(1-theta(0)), phi(0) = 1, gamma(0) = 1, (D(f))(5) = 1, theta(5) = 0, phi(5) = 0, gamma(5) = 0

(5)

dsys := {Eq1, Eq2, Eq3, Eq4, bcs}:

for i to 3 do Bi := VBi[i]; dsol[i] := dsolve(dsys, numeric, continuation = lambda); print(Bi); print(dsol[i](0)) end do

Error, (in dsolve/numeric/bvp) cannot determine a suitable initial profile, please specify an approximate initial solution

 

NULL

NULL

 

Download soret.mw

 

 

i have run higer order nonlinear ode bvp

but cant solve the error

please help me

NULL

restart

with(plots)

Pr := .71; beta := .5; alpha := .1; S := .1; Du := .1; Nb := .1; Nt := .1; Sc := .67; Sr := .1; omega := 1.0; Lb := 1.0; Pe := 1.0; delta := 1.0; Nc := 1.0; p := .1; q := 5; r := 5; s := 5; a := 1; b := 2; epsilon := .1

Eq1 := (101-100*lambda)*(diff(f(eta), `$`(eta, 3)))-theta(eta)*beta*(diff(f(eta), `$`(eta, 2)))/(1+theta(eta)*beta)+(1+theta(eta)*beta)*f(eta)*(diff(f(eta), `$`(eta, 2)))-(1+theta(eta)*beta)*(diff(f(eta), eta))^2-(M-alpha)*(1+theta(eta)*beta)*(diff(f(eta), eta))

(101-100*lambda)*(diff(diff(diff(f(eta), eta), eta), eta))-.5*theta(eta)*(diff(diff(f(eta), eta), eta))/(1+.5*theta(eta))+(1+.5*theta(eta))*f(eta)*(diff(diff(f(eta), eta), eta))-(1+.5*theta(eta))*(diff(f(eta), eta))^2-(M-.1)*(1+.5*theta(eta))*(diff(f(eta), eta))

(1)

Eq2 := (1+epsilon*theta(eta))*(diff(theta(eta), `$`(eta, 2)))+f(eta)*(diff(theta(eta), eta))+epsilon*(diff(theta(eta), eta))^2+Pr*S*theta(eta)+Pr*Du*(diff(phi(eta), `$`(eta, 2)))+Pr*Nb*(diff(theta(eta), eta))*(diff(phi(eta), eta))+Pr*Nt*(diff(theta(eta), eta))^2

(1+.1*theta(eta))*(diff(diff(theta(eta), eta), eta))+f(eta)*(diff(theta(eta), eta))+.171*(diff(theta(eta), eta))^2+0.71e-1*theta(eta)+0.71e-1*(diff(diff(phi(eta), eta), eta))+0.71e-1*(diff(theta(eta), eta))*(diff(phi(eta), eta))

(2)

Eq3 := (diff(phi(eta), `$`(eta, 2)))/Sc+f(eta)*(diff(phi(eta), eta))-omega*(diff(theta(eta), eta))*(diff(phi(eta), eta))-omega*(diff(theta(eta), `$`(eta, 2)))*phi(eta)-delta*phi(eta)+omega*Nc*(diff(theta(eta), `$`(eta, 2)))+Sr*(diff(theta(eta), `$`(eta, 2)))

1.492537313*(diff(diff(phi(eta), eta), eta))+f(eta)*(diff(phi(eta), eta))-1.0*(diff(theta(eta), eta))*(diff(phi(eta), eta))-1.0*(diff(diff(theta(eta), eta), eta))*phi(eta)-1.0*phi(eta)+1.10*(diff(diff(theta(eta), eta), eta))

(3)

Eq4 := diff(chi(eta), `$`(eta, 2))+Lb*f(eta)*(diff(chi(eta), eta))-Pe*(diff(phi(eta), eta))*(diff(chi(eta), eta))-Pe*(diff(phi(eta), `$`(eta, 2)))*chi(eta)

diff(diff(chi(eta), eta), eta)+1.0*f(eta)*(diff(chi(eta), eta))-1.0*(diff(phi(eta), eta))*(diff(chi(eta), eta))-1.0*(diff(diff(phi(eta), eta), eta))*chi(eta)

(4)

VM := [0., .5, 1.0]

etainf := 9

bcs := f(0) = 0, (D(f))(0) = p*(D@@2)(f)*0, theta(0) = 1+q*(D(theta))(0), phi(0) = 1+r*(D(phi))(0), chi(0) = 1+s*(D(chi))(0), D(f)*etainf = b/a, theta(etainf) = 0, phi(etainf) = 0, chi(etainf) = 0

f(0) = 0, (D(f))(0) = 0., theta(0) = 1+5*(D(theta))(0), phi(0) = 1+5*(D(phi))(0), chi(0) = 1+5*(D(chi))(0), 9*D(f) = 2, theta(9) = 0, phi(9) = 0, chi(9) = 0

(5)

dsys := {Eq1, Eq2, Eq3, Eq4, bcs}

for i to 3 do M := VM[i]; dsol[i] := dsolve(dsys, numeric, continuation = lambda); print(M); print(dsol[i](0)) end do

 

 

 

 

hi.please remove error in attached file

thanks...gfhf.mw

using FDM or FEM rather than dsolve?

ode.docxode.docx

Hi, Im now trying to run my code. But it took like years to even getting the results. may I know any solutions on how to get faster results? Because I have run this code for almost 4 hours yet there is still 'Evaluating...' at the corner left. And when I tried to stop the program, it will stop at 'R1...'.

 

Digits := 18;
with(plots):n:=1.4: mu(eta):=(diff(U(eta),eta)^(2)+diff(V(eta),eta)^(2))^((n-1)/(2)):
Eqn1 := 2*U(eta)+(1-n)*eta*(diff(U(eta), eta))/(n+1)+diff(W(eta), eta) = 0;
Eqn2 := U(eta)^2-(V(eta)+1)^2+(W(eta)+(1-n)*eta*U(eta)/(n+1))*(diff(U(eta), eta))-mu(eta)*(diff(U(eta), eta, eta))-(diff(U(eta), eta))*(diff(mu(eta), eta)) = 0;
Eqn3 := 2*U(eta)*(V(eta)+1)+(W(eta)+(1-n)*eta*U(eta)/(n+1))*(diff(V(eta), eta))-mu(eta)*(diff(V(eta), eta, eta))-(diff(V(eta), eta))*(diff(mu(eta), eta)) = 0;
bcs1 := U(0) = 0, V(0) = 0, W(0) = 0;
bcs2 := U(4) = 0, V(4) = -1;
R1 := dsolve({Eqn1, Eqn2, Eqn3, bcs1, bcs2}, {U(eta), V(eta), W(eta)}, initmesh = 30000, output = listprocedure, numeric);
Warning, computation interrupted
for l from 0 by 2 to 4 do R1(l) end do;
plot1 := odeplot(R1, [eta, U(eta)], 0 .. 4, numpoints = 2000, color = red);

 

Thankyou in advance :)

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