## Need Help to Plot BVP graph...

Please i need help to plot the graph of f'' against episoln using the below BVP

HELP.mw

## To find the numerical solutions of system of nonli...

Dears

Hope everything fine with you. I want to solve the attached problem by numarically and want to plot it but failed. Please see the attachement and correct it. I am waiting your positive respone.

System_of_ODEs.mw

With my best regards and sincerely.

School of Mathematical Sciences
Peking University, Beijing, China

## how can i solve the following odes...

i don't know much about maple, i need to solve the following odes system... I study a little on the help page of maple about numeric[midrich] that takes bvp and deal singularity as well but dint know how to used in the following system

odes.mw

## ODE with boundary conditions involving limits...

Respected member!
Please help me to find the solution of attached problem, I am a new user so pleaes forgive any mistakes.

 >

 >
 >
 >
 >
 >
 (1)
 >
 >

## How can I solve Linear ODEs system using matrix me...

$$\textbf{x}' = \begin{bmatrix} -4 & -2 \\ 3 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix}+\begin{bmatrix} -t \\ -2t-1 \end{bmatrix},\textbf{x}(0)=\begin{bmatrix} 3 \\ -5 \end{bmatrix}$$

As I know firstly, when the matrix is denoted by $A$, we must compute $e^{At}$ by diagonalizing $A$: if $A=PDP^{-1}$ for a diagonal $D$ then $e^{At} = P e^{Dt} P^{-1}$ where $e^{Dt}$ is a diagonal matrix with $(e^{Dt})_{ii} = e^{D_{ii} t}$...

How can I write The Maple code? maple.stackexchange)

restart: with(LinearAlgebra):

A := Matrix(2,2,[-4,-2,3,1]);

....

## boundary conditions...

Dear sir in this problem should accept five boundaryconditions but it is not working for five boundary conditions and showing the following error please can you tell why it is like this ??

Error, (in dsolve/numeric/bvp/convertsys) too many boundary conditions: expected 4, got 5
Error, (in plots:-display) expecting plot structures but received: [fplt[1], fplt[2], fplt[3], fplt[4], fplt[5], fplt[6], fplt[7]]
Error, (in plots:-display) expecting plot structures but received: [tplt[1], tplt[2], tplt[3], tplt[4], tplt[5], tplt[6], tplt[7]]

stretching_cylinder_new1.mw

## Does TWS command of Maple solves system of ODEs ?...

Dear all

I am trying to solve system of ODEs by TWS command for traveling wave solution, but an error is showing. When I enter sinlge ODE or PDE the command does not show any error. Why it is showing error for system of ODEs ?

 >
 >
 >
 >
 >

## Method for numerical solving BVP of ODE with disco...

I try to solve numerically a boundary VP for ODE with different order of discontinuity of right part.

Say, the following BVP is given:

y''(x)+y'(x)+y(x)=F(x)

y(0)=1, y(2)=1

Let's use piecewise right part

F  := piecewise(x<=1, -x, x>1, 2*x+(x-1)^2)

The function

piecewise(x<=1, 1-x, x>1, (x-1)^2)

as obviuos, satisfies the BVP exclung the point x=1, where its 1st and 2nd derivatives are discontinuos.

Numerical solution

N0:=6:
equ2 := diff(theta[0](eta), $(eta, 2))+3*f[0](eta)*(diff(theta[0](eta), eta)); Bcs1 := f[0](0) = 0, (D(f[0]))(0) = 0, theta[0](0) = 1, theta[0](inf) = 0, (D(D(f[0])))(inf) = 0; S1 := dsolve({Bcs1, equ1, equ2}, {f[0](eta), theta[0](eta)}, type = numeric, method = bvp[midrich]); proc(x_bvp) ... end; S1(0); [ d [eta = 0., f[0](eta) = 0., ----- f[0](eta) = 0., [ deta d / d \ ----- |----- f[0](eta)| = 0.82449782146165697398999365896678734, deta \ deta / theta[0](eta) = 1.0000000000000000000000000000000000, d ] ----- theta[0](eta) = -0.71098574970825563256340736114251047] deta ] S1(inf); [ [eta = 4., f[0](eta) = 1.7815670728545914261072119522795076, [ d ----- f[0](eta) = 0.51061876174095320088291844433043562, deta d / d \ ----- |----- f[0](eta)| = 0., theta[0](eta) = 0., deta \ deta / d ----- theta[0](eta) = -0.000054818176138173095945902421930470836 deta ] ] ] Pls, I need to find the function of the limit of f[0](eta) at eta tend to infinity. checked equation 45 of the attached document and for the two equation pls checked equation 36 and 37 for the ODE equation solved above. Kuiken_solution for equation 36 and 37.pdf ## combuned solutions... Asked by:  >  >  (1)  >  >  >  >  (2)  >  >  >  >  (3)  >  (4)  >  (5)  >  (6)  >  (7)  >  (8)  >  (9)  >  (10)  >  >  >  >  >  (1)  >  >  >  >  (2)  >  >  >  >  (3)  >  (4)  >  (5)  >  (6)  >  (7)  >  (8)  >  (9)  >  (10)  >  >  >  >  >  (1)  >  >  >  >  (2)  >  >  >  >  (3)  >  (4)  >  (5)  >  (6)  >  (7)  >  (8)  >  (9)  >  (10)  >  >  > Download staganation_point11.mw in this program im trying to combine the result, but it showing some error can help me please ## not executing for three values... Asked by: http://www.sciencedirect.com/science/article/pii/S100757041300508X> restart; > l := 1; p := 1; A := .5; B := .5; pr := 1; n := [.5, 1, 1.5]; M := 0; b := .5; L := 0; s := .5; K := [blue, green]; 1 [0.5, 1, 1.5] [blue, green] > for j to nops(n) do R1 := 2*n[j]/(n[j]+1); R2 := 2*p/(n[j]+1); R3 := 2/(n[j]+1); sol1 := dsolve([diff(diff(diff(f(eta), eta), eta), eta)+f(eta)*(diff(diff(f(eta), eta), eta))+R1*(1-(diff(f(eta), eta))^2)-M*(diff(f(eta), eta)) = 0, diff(diff(theta(eta), eta), eta)+pr*f(eta)*(diff(theta(eta), eta))-R2*pr*(diff(f(eta), eta))*theta(eta)+R3*(A*(diff(f(eta), eta))+B*theta(eta)) = 0, f(0) = 1, (D(f))(0) = L+b*((D@@2)(f))(0), (D(f))(7) = 1, theta(0) = 1+s*(D(theta))(0), theta(7) = 0], numeric, method = bvp); plots[odeplot](sol1, [eta, ((D@@2)(f))(eta)], color = red); fplt[j] := plots[odeplot](sol1, [eta, diff(diff(f(eta), eta), eta)], color = K[j], axes = boxed); fplt[j] := plots[odeplot](sol1, [eta, f(eta)], color = K[j], axes = boxed); tplt[j] := plots[odeplot](sol1, [[eta, theta(eta)]], color = K[j], axes = normal) end do; plots:-display([seq(fplt[j], j = 1 .. nops(n))]); plots:-display([seq(fplt[j], j = 1 .. nops(n))]); plots:-display([seq(tplt[j], j = 1 .. nops(n))]); http://www.sciencedirect.com/science/article/pii/S100757041300508X Dear sir I am trying to plot the following link paper graphs for practice but I getting the plots for only one set of values here in this paper they plotted many so if you dont muned can help in this case. For example in this first graph named as Fig.1. please can you do this favour... and the paper link is http://www.sciencedirect.com/science/article/pii/S100757041300508X ## multiple assignment... Asked by: > restart; > n := [1, 2, 3, 4, 5]; pr := .71; p := 0; q := 0; b := 0; l := 0; s := 0; > for j to nops(n) do R1 := 2*n[j]/(1+n[j]); R2 := 2*p/(1+n); sys := diff(diff(diff(f(eta), eta), eta), eta)+f(eta)*(diff(diff(f(eta), eta), eta))+1-(diff(f(eta), eta))^2 = 0, (diff(diff(theta(eta), eta), eta))/pr+f(eta)*(diff(theta(eta), eta))-R2*(diff(f(eta), eta))*theta(eta) = 0; bcs := f(0) = 0, (D(f))(0) = l+b*((D@@2)(f))(0), (D(f))(-.5) = 1, theta(0) = 1+s*(D(theta))(0), theta(-.5) = 0; proc (f1, th1, { output::name := 'number' }) local res1, fvals, thvals, res2; option remember; res1 := dsolve({sys, f(0) = 0, theta(0) = 1+th1, (D(f))(-2) = f1, (D(theta))(-2) = th1, ((D@@2)(f))(0) = f1-1}, numeric, :-output = listprocedure); fvals := (subs(res1, [seq(diff(f(eta), [$(eta, i)]), i = 0 .. 2)]))(0); thvals := (subs(res1, [seq(diff(theta(eta), [$(eta, i)]), i = 0 .. 1)]))(0); res2 := dsolve({sys, f(0) = fvals[1], theta(0) = thvals[1], theta(1) = 0, (D(f))(0) = fvals[2], (D(f))(1) = 0}, numeric, :-output = listprocedure); if output = 'number' then [fvals[3]-(subs(res2, diff(f(eta), $(eta, 2))))(0), thvals[2]-(subs(res2, diff(theta(eta), eta)))(0)] else res1, res2 end if end proc; p1 := proc (f1, th1) p(args)[1] end proc; p2 := proc (f1, th1) p(args)[2] end proc; p(.3, -.2); par := fsolve([p1, p2], [.3, -.2]); res1, res2 := p(op(par), output = xxx); plots:-display(plots:-odeplot(res1, [[eta, f(eta)], [eta, theta(eta)]]), plots:-odeplot(res2, [[eta, f(eta)], [eta, theta(eta)]])); plots:-display(plots:-odeplot(res1, [[eta, diff(f(eta), eta)], [eta, diff(theta(eta), eta)]]), plots:-odeplot(res2, [[eta, diff(f(eta), eta)], [eta, diff(theta(eta), eta)]])); plots:-display(plots:-odeplot(res1, [[eta, diff(f(eta), eta, eta)]]), plots:-odeplot(res2, [[eta, diff(f(eta), eta, eta)]])); fplt[j] := plots[odeplot](sol1, [eta, diff(diff(f(eta), eta), eta)], color = L[j], axes = boxed); tplt[j] := plots[odeplot](sol1, [[eta, theta(eta)]], color = L[j], axes = boxed) end do;

Dear Sir

In this above problem it showing that error as  Error, cannot split rhs for multiple assignment please can you tell why it is showing like this  ?? and where i did multiple assignments ??