Items tagged with equations equations Tagged Items Feed

Good day everyone, could you please help use Gauss Elimination method for these system of equations. See the worksheet here F1.mw

Thanks.

Dear All,

I am solving 6 ODE equations with boundary conditions using Runge kutta Felbergh 45 (Maple 12). then, i got this problem.. any suggestion??

Thank you :)

ISPC3.mw

``

restart; with(plots); M := 3; k = .2; blt := 6; r := 2; l := .1; Pr := 6.8; Ec := 2; N := .5; rho := .5; Tv := .5; Tt := .5; c := 1; cm := .1; cp := .1

Eq1 := diff(f(eta), eta, eta, eta)+f(eta)*(diff(f(eta), eta, eta))-(diff(f(eta), eta))^2-M*(diff(f(eta), eta))+B*H(eta)*(F(eta)-(diff(f(eta), eta))) = 0;

diff(diff(diff(f(eta), eta), eta), eta)+f(eta)*(diff(diff(f(eta), eta), eta))-(diff(f(eta), eta))^2-3*(diff(f(eta), eta))+B*H(eta)*(F(eta)-(diff(f(eta), eta))) = 0

(1)

Eq2 := G(eta)*(diff(F(eta), eta))+F(eta)^2+B*(F(eta)-(diff(f(eta), eta))) = 0;

G(eta)*(diff(F(eta), eta))+F(eta)^2+B*(F(eta)-(diff(f(eta), eta))) = 0

(2)

Eq3 := G(eta)*(diff(G(eta), eta))+B*(f(eta)+G(eta)) = 0;

G(eta)*(diff(G(eta), eta))+B*(f(eta)+G(eta)) = 0

(3)

Eq4 := G(eta)*(diff(H(eta), eta))+H(eta)*(diff(G(eta), eta))+F(eta)*H(eta) = 0;

G(eta)*(diff(H(eta), eta))+H(eta)*(diff(G(eta), eta))+F(eta)*H(eta) = 0

(4)

Eq5 := diff(theta(eta), eta, eta)+Pr*(f(eta)*(diff(theta(eta), eta))-2*(diff(f(eta), eta))*theta(eta))+N*Pr*(theta1(eta)-theta(eta))/(rho*c*Tt)+N*Pr*Ec*(F(eta)-(diff(f(eta), eta)))^2/(rho*Tv) = 0;

diff(diff(theta(eta), eta), eta)+6.8*f(eta)*(diff(theta(eta), eta))-13.6*(diff(f(eta), eta))*theta(eta)+13.60000000*theta1(eta)-13.60000000*theta(eta)+27.20000000*(F(eta)-(diff(f(eta), eta)))^2 = 0

(5)

Eq6 := 2*F(eta)*theta1(eta)+G(eta)*(diff(theta1(eta), eta))+cp*(theta1(eta)-theta(eta))/(c*cm*Tt) = 0;

2*F(eta)*theta1(eta)+G(eta)*(diff(theta1(eta), eta))+2.000000000*theta1(eta)-2.000000000*theta(eta) = 0

(6)

bcs1 := f(0) = r, (D(f))(0) = -1, (D(f))(blt) = 0, F(blt) = 0, G(blt) = -f(blt), H(blt) = k, theta(0) = 1, theta(blt) = 0, theta1(blt) = 0;

f(0) = 2, (D(f))(0) = -1, (D(f))(6) = 0, F(6) = 0, G(6) = -f(6), H(6) = k, theta(0) = 1, theta(6) = 0, theta1(6) = 0

(7)

L := [0.1e-2];

[0.1e-2]

(8)

for k to 1 do R := dsolve(eval({Eq1, Eq2, Eq3, Eq4, Eq5, Eq6, bcs1}, B = L[k]), [f(eta), F(eta), G(eta), H(eta), theta(eta), theta1(eta)], numeric, output = listprocedure); Y || k := rhs(R[2]); YP || k := rhs(R[3]); YR || k := rhs(R[4]); YQ || k := rhs(R[5]) end do

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

 

R

R

(9)

print([(YP || (1 .. 1))(0)]);

[YP1(0)]

(10)

``

P1 := plot([YP || (1 .. 1)], 0 .. 14, labels = [eta, (D(f))(eta)]):

Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

 

plots:-display([P1]);

 

``

``


Download ISPC3.mw

D_Method.mw

The classical Draghilev’s method.  Example of solving the system of two transcendental equations. For a single the initial approximation are searched 9 approximate solutions of the system.
(4*(x1^2+x2-11))*x1+2*x1+2*x2^2-14+cos(x1)=0;
2*x1^2+2*x2-22+(4*(x1+x2^2-7))*x2-sin(x2)=0; 
x01 := -1.; x02 := 1.;

Hi there,

I would like to compute and display the nullclines of a set of ordinary differential equations.

AFAIK, I can compute the nullclines in Maple by defining the equations and solving the system

e.g.:

# Define the equations
eq1 := u(t)*(1-u(t)/kappa)-u(t)*v(t) = 0;
eq2 := g*(u(t)-1)*v(t) = 0;

# Solve the system (i.e. compute the nullclines)
sol := solve({eq1, eq2}, {u(t), v(t)});

However, I am not quite able to imagine how to display them over a dfieldplot or a phaseportrait.

Attached is an example with some differential equations, and their vector field and trajectories: MaplePrimes_Predator_prey_model_nullclines.mw.

It can be use to illustrate how to (compute and) display the nullclines.

 

Thank you,

jon


Equation: ((x1+.25)^2+(x2-.2)^2-1)^2+(x3-.1)^2-.999=0;



a_cam_3D.mw


Cam mechanism animation.   Equation:  (xx2-1.24)^10+5*(xx1-.66)^10-9.=0
a_cam.mw

Hi i 2 questions. all pertaining to solving a systems of equations mod 2

First if i have a large set of equations, 11^3 equations in 11 unknowns and i want maple to give me ALL solutions mod 2 how can i do that? Maples msolve is loosing solutions.

Second suppose i want all unique solutions that say 6 of the variables can have but dont care what the solution to the other variables are as long as it is a solution. 

mini example:

say x=1,y=1,z=1 is a solution as well as x=1,y=1,z=0, i just want to know about x=1,y=1.

 

Hi,

I'm a newer of maple .I want to prove x=z,y=z from equations of parametric z.But maple don't solve what I want,who can give me a help .thank you

 

Hello,

Im solving 4 ODE equations with BC. im trying to shoot the initial value but im having this error:

""Error, (in isolate) cannot isolate for a function when it appears with different arguments""

anyone could help me???

shooting92.mw

``

restart

Shootlib := "E:\\shooting/":

libname := Shootlib, libname:

with(Shoot):

with(plots):

n := 2:

FNS := {F(eta), H(eta), f(eta), g(eta), u(eta), v(eta)}:

ODE := {g(eta)*(diff(g(eta), eta))+B*(f(eta)+g(eta)) = 0, g(eta)*(diff(F(eta), eta))+F(eta)^2+B*(F(eta)-u(eta)) = 0, g(eta)*(diff(H(eta), eta))+H(eta)*(diff(g(eta), eta))+F(eta)*H(eta) = 0, diff(v(eta), eta)+f(eta)*v(eta)-u(eta)^2+B*H(eta)*(F(eta)-u(eta))-M*u(eta) = 0, diff(f(eta), eta) = u(eta), diff(u(eta), eta) = v(eta)};

{g(eta)*(diff(H(eta), eta))+H(eta)*(diff(g(eta), eta))+F(eta)*H(eta) = 0, g(eta)*(diff(g(eta), eta))+0.2e-1*f(eta)+0.2e-1*g(eta) = 0, g(eta)*(diff(F(eta), eta))+F(eta)^2+0.2e-1*F(eta)-0.2e-1*u(eta) = 0, diff(v(eta), eta)+f(eta)*v(eta)-u(eta)^2+0.2e-1*H(eta)*(F(eta)-u(eta))-3*u(eta) = 0, diff(f(eta), eta) = u(eta), diff(u(eta), eta) = v(eta)}

(1)

IC := {F(0) = gamma, H(0) = Q, f(0) = 0, g(0) = z, u(0) = 1, v(0) = alpha};

{F(0) = gamma, H(0) = Q, f(0) = 0, g(0) = z, u(0) = 1, v(0) = alpha}

(2)

BC := {F(L) = 0, H(L) = n, g(L) = -f(L), u(L) = 0};

{F(6) = 0, H(6) = 2, g(6) = -f(6), u(6) = 0}

(3)

infolevel[shoot] := 1:

S := shoot(ODE, IC, BC, FNS, [alpha = 0, gamma = 0, z = -.2, Q = 0])

Error, (in isolate) cannot isolate for a function when it appears with different arguments

 

``

``


Download shooting92.mw

Hello,

      I would like to solve a system of 9 nonlinear equations, with the constraints on all 9 variables to be that they are nonnegative. How can I do this?

My code is below - I am trying NLPSolve and have tried solve, but am getting stuck.

with(Optimization);

restart; eq1 := 531062-S/(70*365)-(.187*(1/365))*(H+C+C1+C2)*S/N = 0;eq2 := (4/365*(T+C))*S/N-(.187*(1/365))*(H+C+C1+C2)*T/N-(1/(70*365)+1/(5*365))*T = 0; eq3 := (.187*(1/365))*(H+C+C1+C2)*S/N-(4/365)(T+C)*H/N-(1/(70*365)+1/(4*365))*H = 0; eq4 := (.187*(1/365))*(H+C+C1+C2)*T/N+(4/365*(T+C))*H/N-(1/(70*365)+3/(8*365)+.2*(1/365)+.1)*C = 0; eq5 := .1*C-(1/(70*365)+1/(4*365)+1/60+.5)*C1 = 0; eq6 := (1/60)*C1-(1/(70*365)+1/(4*365)+1/210+.5)*C2 = 0; eq7 := .5*C1-(1/(70*365)+1/60+0.1e-2)*CT1 = 0; eq8 := .5*C2-(1/(70*365)+1/210+(1/9)*(0.1e-2*7))*CT2+(1/60)*CT1 = 0; eq9 := N-S-T-H-C-C1-C2-CT1-CT2 = 0; soln := NLPSolve({eq1, eq2, eq3, eq4, eq5, eq6, eq7, eq8, eq9}, {C, C1, C2, CT1, CT2, H, N, S, T}, assume = nonnegative);

Hi all

I'm having a hard time, making Maple plot a pretty huge expression in my project.

I have solved a differential equation with initial conditions with method=laplace. The differential equation contains a fourier serie equation, so the more accurate i want the equation to be, the larger the differential equation will be.

Maple solves the equation just fine, and i can plot the solution with 2-4 fourier parts, but when i go higher as i need, the graph ends up empty?

with 20 parts i get the following equation: 

0.*sin(52.88*t)+0.*cos(74.03*t)-0.*sin(74.03*t)-0.*cos(52.88*t)+0.*cos(200.95*t)-0.*sin(200.95*t)+0.*cos(158.65*t)-5.55*10^(-8)*sin(105.76*t)-0.*sin(116.34*t)+0.*cos(31.73*t)-.45*sin(10.58*t)+1.02*cos(10.58*t)+0.*sin(95.19*t)+0.*cos(116.34*t)+0.*sin(179.80*t)-0.*cos(179.80*t)+0.*sin(137.49*t)-0.*sin(31.73*t)-0.*cos(95.19*t)+5.53*10^(-993)*(-1.13*10^992*cos(10.61*t)+8.14*10^991*sin(10.61*t))*exp(-0.7e-1*t)+4.23*10^(-7)*cos(211.53*t)-6.69*10^(-7)*cos(63.46*t)-6.11*10^(-7)*cos(105.76*t)+5.79*10^(-7)*cos(126.92*t)+6.67*10^(-8)*sin(42.31*t)-5.88*10^(-8)*sin(148.07*t)+5.88*10^(-8)*sin(211.53*t)+7.09*10^(-7)*cos(42.31*t)+5.45*10^(-8)*sin(84.61*t)+6.40*10^(-7)*cos(84.61*t)+5.72*10^(-8)*sin(126.92*t)-9.01*10^(-7)*cos(21.15*t)+5.97*10^(-8)*sin(169.22*t)+5.06*10^(-7)*cos(169.22*t)-5.98*10^(-8)*sin(190.38*t)-4.65*10^(-7)*cos(190.38*t)-5.44*10^(-7)*cos(148.07*t)-1.33*10^(-7)*sin(21.15*t)-5.61*10^(-8)*sin(63.46*t)-0.*cos(137.49*t)-0.*sin(158.65*t)

if i plot that expression, the graph ends up empty?

I did also try to solve the equation numerical to plot it with odeplot, but when i try to solve it without the laplace method i get this error message:
"Error, (in dsolve) found the following equations not depending on the unknows of the input system:"

The differential equation is:

ode:=diff(Theta(t), t, t)+2*Zeta*omega[balanceue]*(diff(Theta(t), t))+omega[balanceue]^2*Theta(t) = M[p]/m[balanceue]

and the initial conditions:

ICS := Theta(0) = (1/8)*Pi, (D(Theta))(0) = 0;

when i do:

dsolve({ICS, ode}, Theta(t), method = laplace) it solves just fine.

 

but when i try with:

dsolve({ICS, ode}, Theta(t))

or

dsolve({ICS, ode}, Theta(t),numeric)

I get the message: 

Error, (in dsolve) found the following equations not depending on the unknowns of the input system: {Theta(0) = (1/8)*Pi, (D(Theta))(0) = 0}

It doesnt seem logical at all, is it a bug? Or can anybody help me with this problem?


Regards

Nicolai

I have a nonlinear system with 4 equations and 4 unknowns. I am using fsolve. I know that there are multiple solutions for each variable but am only getting one. I need the others. what do I do??

This is my code:

R__1 := Matrix([[1, 0] , [0, 1] ]);

R__2 := Matrix([[1/2, sqrt(3)/2] , [-sqrt(3)/2, 1/2] ]);

R__3 := Matrix([[-1/2, sqrt(3)/2] , [-sqrt(3)/2, -1/2] ]);

R__4 := Matrix([[-1, 0] , [0, -1] ]);

R__5 := Matrix([[-1/2, -sqrt(3)/2] , [sqrt(3)/2, -1/2] ]);

 

d__1 := Vector( [ 0, 5.4] );

d__2 := Vector( [ 6.4, 4.539] );

d__3 := Vector( [ 11, 4.078] );

d__4 := Vector( [ 15.5, 2.079] );

d__5 := Vector( [ 19, 1.039] );

 

a := Vector( [ a__x, a__y] );

 

A__1:=R__1.a+d__1;

A__2:=R__2.a+d__2;

A__3:=R__3.a+d__3;

A__4:=R__4.a+d__4;

A__5:=R__5.a+d__5;

 

OO:=Vector([O__x,O__y]);

 

DA1:=A__2.A__2-A__1.A__1-2*(A__2-A__1).OO;

DA2:=A__3.A__3-A__1.A__1-2*(A__3-A__1).OO;

DA3:=A__4.A__4-A__1.A__1-2*(A__4-A__1).OO;

DA4:=A__5.A__5-A__1.A__1-2*(A__5-A__1).OO;

 

fsolve({DA1,DA2,DA3,DA4},{a__x,a__y,O__x,O__y});

Thanks for any tips you may be able to offer

 

How do I plot the following equations in Maple ?:

I already tried this: 

 

According to the given solution the plot should look like that: 

I think I have to tell maple that the function is defined from R^2 -> R, but I don't know how to do this. 

Thanks in advance for your kind help.

 

1 2 3 4 5 6 7 Last Page 3 of 54