## iterative method for nonlinear equation...

Asked by:

hy

i have to develop a code i which i have system of nonlinear equation

i have to generate the matrix of that nonlinear equation then i want to do or apply any method say newton method and make a loop which help us to find a solution using some tolerance

at the end i get a result in form of a table which give nth matrix then value of function matrix at nth value then error i-e xn-x(n-1)

thanx in advance

## error for dsolve differential equation.......

Asked by:

hi..i have a problem for solving this nonlinear differential equationerror.mw

 (1)

 (2)

############################################################CHANGE OF VARIABLE:::           x=y*L

Download error.mw

please help me

thanks...

## ODE non linear first order...

Asked by:

Dear all,

I would like to solve the following non linear ODE with Maple, but I am no able. I do not know if it is possible, beccause it is nolinear.

I really appreciate any advice or help. This is the equation:

y'(x) - (Q - x*p0*(exp(alpha-beta*y(x)))/(1+exp(alpha-beta*y(x))))^2=0

thanks a lot

## Nonlinear Coupled PDE...

Asked by:

Hy Prof.

Please help me or guide me to get idea to solve Nonlinear coupled PDEwith MAPLE.Dr.Sam Dao could please help me as I saw your YOUTUBE lecturer which very helpful to me and please give some idea about my topic.

pde[1] := diff(u(x, t), t)-D(diff(u(x, t), x, x)) = alpha*u(x, t)*(1-v(x, t))

pde[2] := diff(v(x, t), t)-E(diff(v(x, t), x, x)) = beta*v(x, t)*(1-u(x, t))

Thanks in advance and answer is highly appricaited

## how i can pdsolve this nonlinear equations...

Asked by:

hi...please help me for solve this nonlinear equations with pdsolve

thanksoffcenter2.mw

 (1)

 (2)

 (3)

#####################################

 (4)

at x=

 (5)

 (6)

 (7)

############################################

at x=0

 (8)

 (9)

################################################

at t=0 for x= [0,La]

 (10)

 (11)

 (12)

 (13)

 (14)

 (15)

 (16)

######################################################

at t=0 for x= [0,La)

 (17)

 (18)

###################################################

at t=0 for x=La

 (19)

 (20)

Download offcenter2.mw

## HELP : got unable to store error...

Asked by:

Hi everyone!

I have a problem solving the nonlinear ode (as attached below). I got this error ---> Error, (in fproc) unable to store '-1.32352941215398+(-0.441176470717993e-1, -0.)' when datatype=float[8]

1) Could someone please explain to me what does the unable store .... error means?

and i will be grateful if you could help me finding the solution out. Thanks in advance

## Solving a nonlinear system of 4 equations using sh...

Asked by:

Dear All,

I have a problem solving the attached nonlinear system of equations using shooting method.
I will be grateful if you could help me finding the solutions out.

restart; Shootlib := "C:/Shoot9"; libname := Shootlib, libname; with(Shoot);
with(plots);
N1 := 1.0; N2 := 2.0; N3 := .5; Bt := 6; Re_m := N1*Bt; gamma1 := 1;
FNS := {f(eta), fp(eta), fpp(eta), g(eta), gp(eta), m(eta), mp(eta), n(eta), np(eta), fppp(eta)};
ODE := {diff(f(eta), eta) = fp(eta), diff(fp(eta), eta) = fpp(eta), diff(fpp(eta), eta) = fppp(eta), diff(g(eta), eta) = gp(eta), diff(gp(eta), eta) = N1*(2.*g(eta)+(eta-2.*f(eta)).gp(eta)+2.*g(eta)*fp(eta)+2.*N2.N3.(m(eta).np(eta)-n(eta).mp(eta))), diff(m(eta), eta) = mp(eta), diff(mp(eta), eta) = Re_m.(m(eta)+(eta-2.*f(eta)).mp(eta)+2.*m(eta)*fp(eta)), diff(n(eta), eta) = np(eta), diff(np(eta), eta) = Re_m.(2.*n(eta)+(eta-2.*f(eta)).np(eta)+2.*N2/N3.m(eta).gp(eta)), diff(fppp(eta), eta) = N1*(3.*fpp(eta)+(eta-2.*f(eta)).fppp(eta)-2.*N2.N2.m(eta).(diff(mp(eta), eta)))};
blt := 1.0; IC := {f(0) = 0, fp(0) = 0, fpp(0) = alpha1, g(0) = 1, gp(0) = beta1, m(0) = 0, mp(0) = beta2, n(0) = 0, np(0) = beta3, fppp(0) = alpha2};
BC := {f(blt) = .5, fp(blt) = 0, g(blt) = 0, m(blt) = 1, n(blt) = 1};
infolevel[shoot] := 1;
S := shoot(ODE, IC, BC, FNS, [alpha1 = 1.425, alpha2 = .425, beta1 = -1.31, beta2 = 1.00, beta3 = 1.29]);
Error, (in isolate) cannot isolate for a function when it appears with different arguments
p := odeplot(S, [eta, fp(eta)], 0 .. 15);
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution
display(p);
Error, (in plots:-display) expecting plot structure but received: p
p2 := odeplot(S, [eta, theta(eta)], 0 .. 10);
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution
display(p2);
Error, (in plots:-display) expecting plot structure but received: p2

## nonlinear curve fit...

Asked by:

Dear Community,

I've made a nonlinear curve fit with the Minimize routine (see attachment). What would be an easy and elegant way to rerun the model (Model) with the fitted values of a, b, c and plot the result together with the measured points in the same chart? I'm stuck here.

Tx in advance,

best regards

Andras

BroSzem_Data.xlsx

Nonlin_Curve_Fit.mw

## Linkage mechanisms

by: Maple 15

General description of the method of solving underdetermined systems of equations. As a particular application of the idea proposed a universal method  kinematic analysis for all kinds of linkage (lever) mechanisms. With the description and examples.
The method can be used for powerful CAD linkages.

Description: Calculation_method_of_linkages.pdf

## solving system of non linear equations...

Asked by:

hello every one.please help me with solving this equations.i can not solve this and i need it.thanks

eq1 := (cos(beta2)-1)*w11-sin(beta2)*w12+(cos(alpha2)-1)*z11-sin(alpha2)*z12-cos(delta2) = 0; eq2 := (cos(beta2)-1)*w12+sin(beta2)*w11+(cos(alpha2)-1)*z12+sin(alpha2)*z11-2*sin(delta2) = 0; eq3 := (cos(beta3)-1)*w11-sin(beta3)*w12+(cos(alpha3)-1)*z11-sin(alpha3)*z12-3*cos(delta3) = 0; eq4 := (cos(beta3)-1)*w12+sin(beta3)*w11+(cos(alpha3)-1)*z12+sin(alpha3)*z11-4*sin(delta3) = 0; eq5 := (cos(beta4)-1)*w11-sin(beta4)*w12+(cos(alpha4)-1)*z11-sin(alpha4)*z12-5*cos(delta4) = 0; eq6 := (cos(beta4)-1)*w12+sin(beta4)*w11+(cos(alpha4)-1)*z12+sin(alpha4)*z11-6*sin(delta4) = 0; eq7 := (cos(beta5)-1)*w11-sin(beta5)*w12+(cos(alpha5)-1)*z11-sin(alpha5)*z12-7*cos(delta5) = 0; eq8 := (cos(beta5)-1)*w12+sin(beta5)*w11+(cos(alpha5)-1)*z12+sin(alpha5)*z11-8*sin(delta5) = 0; alpha2 := -20; alpha3 := -45; alpha4 := -75; alpha5 := -90; delta2 := 15.5; delta3 := -15.9829; delta4 := -13.6018; delta5 := -16.7388; P21 = .5217; P31 = 1.3421; P41 = 2.3116; P51 = 3.1780;

## Equidistant curves

by: Maple 15

equidistant_curve_MP.mw  Equidistant curves to the curves on the surface. (Without any sense, but real.)

## ODE boundary value problem ...

Asked by:

It is known that ODE boundary value problem is similar to the problem of solving systems of nonlinear equations. Equations are the boundary conditions, and the variables are the values of the initial data.
For example:

y '' = f (x, y, y '), 0 <= x <= 1,

y (0) = Y0, y (1) = Y1;

Where y (1) = Y1 is the equation, and Z0 is variable, (y '(0) = Z0).

solve () and fsolve () are not directly suitable for such tasks. Directly should work the package of optimization in relation to a system of nonlinear equations. (Perhaps it has already been implemented in Maple.)
Personally, I am very small and unprofessional know Maple and cannot do it. Maybe there is someone who would be interested, and it will try to implement this approach to solving ODE boundary value problems?

## Solving with HPM...

Asked by:

Hi everyone. I'm going to solve a problem of an article with hpm. well I wrote some initial codes(I uploaded both codes and article). but now I face with a problem. I cant reach to the correct plot that is in the article. could you please help me???

(dont think I am lazy ;))) I found f and g (by make a system with A1 and B1 and solve it i found f[0] and g[0], with p^3 coefficient in A-->f[1] and then with B2 I foud g[1]) and their plot was correct. but the problem is theta and phi and their plots :(( )

Project.mw

2.pdf   this is article

 > restart;
 > lambda:=0.5;K[r]:=0.5;Sc:=0.5;Nb:=0.1;Nt:=0.1;Pr:=10;
 (1)
 > equ1:=diff(f(eta),eta\$4)-R*(diff(f(eta),eta)*diff(f(eta),eta\$2)-f(eta)*diff(f(eta),eta\$2))-2*K[r]*diff(g(eta),eta)=0; equ2:=diff(g(eta),eta\$2)-R*(diff(f(eta),eta)*g(eta)-f(eta)*diff(g(eta),eta))+2*K[r]*diff(f(eta),eta)=0; equ3:=diff(theta(eta),eta\$2)+Pr*R*f(eta)*diff(theta(eta),eta)+Nb*diff(phi(eta),eta)*diff(theta(eta),eta)+Nt*diff(theta(eta),eta)^2=0; equ4:=diff(phi(eta),eta\$2)+R*Sc*f(eta)*diff(phi(eta),eta)+diff(theta(eta),eta\$2)*(Nt/Nb)=0;
 (2)
 > ics:= f(0)=0,D(f)(0)=1,g(0)=0,theta(0)=1,phi(0)=1; f(1)=lambda,D(f)(1)=0,g(1)=0,theta(1)=0,phi(1)=0;
 (3)
 > hpm1:=(1-p)*(diff(f(eta),eta\$4)-2*K[r]*diff(g(eta),eta))+p*(diff(f(eta),eta\$4)-R*(diff(f(eta),eta)*diff(f(eta),eta\$2)-f(eta)*diff(f(eta),eta\$2))-2*K[r]*diff(g(eta),eta))=0; hpm2:=(1-p)*(diff(g(eta),eta\$2)+2*K[r]*diff(f(eta),eta))+p*(diff(g(eta),eta\$2)-R*(diff(f(eta),eta)*g(eta)-f(eta)*diff(g(eta),eta))+2*K[r]*diff(f(eta),eta))=0; hpm3:=(1-p)*(diff(theta(eta),eta\$2))+p*(diff(theta(eta),eta\$2)+Pr*R*f(eta)*diff(theta(eta),eta)+Nb*diff(phi(eta),eta)*diff(theta(eta),eta)+Nt*diff(theta(eta),eta)^2)=0; hpm4:=(1-p)*(diff(phi(eta),eta\$2)+diff(theta(eta),eta\$2)*(Nt/Nb))+p*(diff(phi(eta),eta\$2)+R*Sc*f(eta)*diff(phi(eta),eta)+diff(theta(eta),eta\$2)*(Nt/Nb))=0;
 (4)
 > f(eta)=sum(f[i](eta)*p^i,i=0..1);
 (5)
 > g(eta)=sum(g[i](eta)*p^i,i=0..1);
 (6)
 > theta(eta)=sum(theta[i](eta)*p^i,i=0..1);
 (7)
 > phi(eta)=sum(phi[i](eta)*p^i,i=0..1);
 (8)
 > A:=collect(expand(subs(f(eta)=f[0](eta)+f[1](eta)*p,g(eta)=g[0](eta)+g[1](eta)*p,hpm1)),p);
 (9)
 > A1:=diff(f[0](eta),eta\$4)-2*K[r]*(diff(g[0](eta),eta))=0; A2:=diff(f[1](eta),eta\$4)-2*K[r]*(diff(g[1](eta),eta))-R*(diff(f[0](eta),eta))*(diff(f[0](eta),eta\$2))+R*f[0](eta)*(diff(f[0](eta),eta\$2))=0;
 (10)
 > icsA1:=f[0](0)=0,D(f[0])(0)=1,g[0](0)=0,f[0](1)=lambda,D(f[0])(1)=0,g[0](1)=0; icsA2:=f[1](0)=0,D(f[1])(0)=0,g[1](0)=0,f[1](1)=0,D(f[1])(1)=0,g[1](1)=0;
 (11)
 > B:=collect(expand(subs(f(eta)=f[0](eta)+f[1](eta)*p,g(eta)=g[0](eta)+g[1](eta)*p,hpm2)),p);
 (12)
 > B1:=diff(g[0](eta),eta\$2)+2*K[r]*(diff(f[0](eta),eta))=0; B2:=diff(g[1](eta),eta\$2)+2*K[r]*(diff(f[1](eta),eta))-R*(diff(f[0](eta),eta))*g[0](eta)+R*f[0](eta)*(diff(g[0](eta),eta))=0;
 (13)
 > icsB1:=f[0](0)=0,D(f[0])(0)=1,g[0](0)=0,f[0](1)=lambda,D(f[0])(1)=0,g[0](1)=0; icsB2:=f[1](0)=0,D(f[1])(0)=0,g[1](0)=0,f[1](1)=0,D(f[1])(1)=0,g[1](1)=0;
 (14)
 > C:=collect(expand(subs(theta(eta)=theta[0](eta)+theta[1](eta)*p,phi(eta)=phi[0](eta)+phi[1](eta)*p,f(eta)=f[0](eta)+f[1](eta)*p,hpm3)),p);
 (15)
 > C1:=diff(theta[0](eta),eta\$2)=0; C2:=diff(theta[1](eta), eta, eta)+Pr*R*f[0](eta)*(diff(theta[0](eta), eta))+Nb*(diff(phi[0](eta), eta))*(diff(theta[0](eta), eta))+Nt*(diff(theta[0](eta), eta))^2=0;
 (16)
 > icsC1:=theta[0](0)=1,theta[0](1)=0; icsC2:=f[0](0)=0,D(f[0])(0)=1,f[1](1)=0,D(f[1])(1)=0,theta[1](0)=0,theta[1](1)=0,phi[0](0)=0,phi[0](1)=0;
 (17)
 > E:=collect(expand(subs(theta(eta)=theta[0](eta)+theta[1](eta)*p,phi(eta)=phi[0](eta)+phi[1](eta)*p,f(eta)=f[0](eta)+f[1](eta)*p,hpm4)),p);
 (18)
 > E1:=diff(phi[0](eta),eta\$2)+Nt*(diff(theta[0](eta),eta\$2))/Nb=0; E2:=diff(phi[1](eta),eta\$2)+Nt*(diff(theta[1](eta),eta\$2))/Nb+R*Sc*f[0](eta)*(diff(phi[0](eta),eta))=0;
 (19)
 > icsE1:=phi[0](0)=1,phi[0](1)=0; icsE2:=f[0](0)=0,D(f[0])(0)=1,f[1](1)=0,D(f[1])(1)=0,theta[1](0)=0,theta[1](1)=0,phi[1](0)=0,phi[1](1)=0;
 (20)
 >

Download Project.mw

Project.mw

Download Project.mw

thanks for your favorits

## Problem with HPM...

Asked by:

Hi everyone.

I'm going to solve a problem with HPM in Maple. I wrote some initial codes but now I'm confused becouse of P^0 coefficients in A1 and B1. I mean I can't reach to f0 and g0.

I upload that file. these are codes that i typed. could you please help me how can I reach to them(f0 & g0)?

http://www.filehosting.org/file/details/573095/Maple%20Project+.mw

## Equidistant surface

by: Maple 15

Example of the equidistant surface at a distance of 0.25 to the surface
x3
-0.1 * (sin (4 * x1) + sin (3 * x2 + x3) + sin (2 * x2)) = 0
Constructed on the basis of universal parameterization of surfaces.

equidistant_surface.mw

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