# Items tagged with initialinitial Tagged Items Feed

### Solve Transport / Advection Equation...

August 05 2015
1 8

Dear all,

I am trying to solve the following partial differential equation (transport or advection equation) with given initial and boundary conditions:

restart: with(PDEtools):
sys := [v*diff(u(x,t), x) + diff(u(x,t), t) = 0, u(x,0) = exp(-x), u(0,t) = sin(t)];
pdsolve(sys);

But it does not work. The solution is (or should be):

u(x, t) = exp(t*v-x)+Heaviside(t-x/v)*(sin(t-x/v)-exp(t*v-x))

I think the reason is that the interval for t (in [0, inf)) and x (in [0, 1]) is not specified. On the other hand, this works:

restart: with(PDEtools):
sys := [diff(u(x, t), t) = diff(u(x, t), x, x), u(0, t) = 0, u(1, t) = 0, u(x,0) = f(x)];
sol := pdsolve(sys);

How can I solve a PDE like the transport equation with given initial AND boundary conditions?

Thanks a lot

### Vibrations with maple...

February 26 2015 Maple 18
0
0

In this section, we will consider several linear dynamical systems in which each mathematical model is a differential equation of second order with constant coefficients with initial conditions specifi ed in a time that we take as t = t0.

All in maple.

Vibraciones.mw

(in spanish)

Atte.

L.AraujoC.

### Error, (in isolate) cannot isolate for a function ...

December 10 2014
0 12

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???

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 (1)
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 (2)
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 (3)
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 Error, (in isolate) cannot isolate for a function when it appears with different arguments
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### Solving ODE by Laplace transform...

November 22 2014
0 2

I am trying to recreate journal work for validating using another computer program so I am trying to use maple to solve the ODE, based on further research I found using laplace might be the best but I am having some trouble.

eq8:=d*(n(t)+C(t))/drho = -rho(t)/(l*alpha*K_c)

given the initial conditions of:

ICs:= n(0) = n_0, rho(0) = rho_0, C(0) = (beta-rho_0)*n_0/(l*lambda)

therefore:

equation9 := dsolve({equation8, ICs}, {C(t), n(t)}, method = laplace)

Following this process I get the error:

Error, (in dsolve) invalid initial condition

According to the journal work the solution I am looking for is:

C(t)=-n(t)+(rho_0^2+rho(t)^2)/(2*l*alpha*K_c)+((Beta+l*lambda-rho_0)*n_0)/(l*lambda)

is there something that I'm doing wrong or missing?

Any help would be greatly Appreciated!

### Solving system of ODEs by Laplace transform...

October 11 2014
0 1

I'm trying to solve this system of ODEs by Laplace transform.

> de1 := d^2*y(t)/dt^2 = y(t)+3*x(t)

> de2 := d^2*x(t)/dt^2 = 4*y(t)-4*exp(t)

with initial conditions

> ICs := y(0) = 2, (D(y))(0) = 3, x(0) = 1, (D(x))(0) = 2

Using

> deqns := de1, de2

and

> var := y(t), x(t)

I need to solve it for both y(t) and x(t), I have tried this by:

> dsolve({ICs, deqns}, var, method = laplace)

And

> dsolve({ICs, deqns}, y(t), method = laplace)

> dsolve({ICs, deqns}, x(t), method = laplace)

However I get this error message:

Error, (in dsolve/process_input) invalid initial condition

Any help is appreciated

### System of PDE with initial condition...

August 01 2014
0 3

How can I solve this problem on Maple?
Can anyone help me please ... I wrote another post before but I can not solve the problem.

lambda is an experimental parameter. I have this initial condition n(x,0)=0.4, c(x,0)=0.

Thanks to everyone

### Pde system with initial condition...

July 27 2014
1 8

Dear Maple Users,

I'm beginner in Maple.

I have this system of Pde:

with lambda experimental parameter and n,c,v dependent variables. I write this on Maple but I read on internet that the solution "float(undefined)" is an error.

I will insert this initial condition: c(x,0)=0,n(x,0)=0.4

Thanks everybody

### trying to generate a code for an initial state...

June 04 2014
0 0

I was given that solitary initial state to see how it will deform as time goes on. am struggling to get my code so that I can get video frames. please help on how I can generate my code

uo(x)= a0x2(1-x)2 for x (less than or equal to) x (less than or equal) 1

u0(x)    = 0 for x > 1

the video clips will be representing the function u(*,t) :x to u(x,t)

for a sequence of choices of t such as t=0; t=0,5...t=3

### Having Problems with dsolve - Error, unable to mat...

May 15 2014
1 2

restart;
Eq1 := diff(T1(t), t) = (W*Cp*(To-T1(t))+UA*(Ts-T1(t)))/(M*Cp);
Eq2 := diff(T2(t), t) = (W*Cp*(T1(t)-T2(t))+UA*(Ts-T2(t)))/(M*Cp);
Eq3 := diff(T3(t), t) = (W*Cp*(T2(t)-T3(t))+UA*(Ts-T3(t)))/(M*Cp);
sys := Eq1, Eq2, Eq3;

Operational Veriables

W := 100;
UA := 10;
Cp := 2;
M := 1000;
To := 20;
Ts := 250;

Initial Conditions

sys1 := {Eq1, Eq2, Eq3};

nsys := nops(sys1);

ics := {T1(0) = 20, T2(0) = 20, T3(0) = 20};
{T1(0) = 20, T2(0) = 20, T3(0) = 20}
nics := nops(ics);
for i from 1 to nics do Sol ||i:=dsolve({sys1, ics[i]},{T1(t),T2(t),T3(t)},numeric)od;
Error, unable to match delimiters
Typesetting:-mambiguous(Typesetting:-mambiguous( for i from 1 to

nics do Sol verbarverbariAssigndsolvelpar(sys1comma ics(i))

commalcubT1(t)commaT2(t)commaT3(t)rcubcommanumericrparod,

Typesetting:-merror("unable to match delimiters")))

### Optimization [Minimize] and [Maximize] with Pi...

April 20 2014
2 3

what is the wrong with Pi set ::: in this function ::: Warning, no iterations performed as initial point satisfies first-order conditions

Optimization[Minimize](x^2 + y^2 + 25*(sin(x)^2+sin(y)^2), x=-2*Pi .. 2*Pi , y= -2*Pi .. 2*Pi);

Warning, no iterations performed as initial point satisfies first-order conditions
[0., [x = HFloat(0.0), y = HFloat(0.0)]]

Optimization[Maximize](x^2 + y^2 + 25*(sin(x)^2+sin(y)^2), x=-2*Pi .. 2*Pi , y= -2*Pi .. 2*Pi);

Warning, no iterations performed as initial point satisfies first-order conditions
[-0., [x = HFloat(0.0), y = HFloat(0.0)]]

--------------------------------

I got my good result when I apply it with this function :

f:= (x,y)->cos(x)*sin(y) -(x/(y^2+1));

Optimization[Maximize](f(x,y), x = -1 .. 2, y = -1 .. 1);

[0.994945017202501170,[x = HFloat(-0.6362676080636113), y = HFloat(1.0)]]

Optimization[Minimize](f(x,y), x = -1 .. 2, y = -1 .. 1);

[-2.02180678335978703,[x = HFloat(2.0), y = HFloat(0.10578346945175972)]]

### Error, (in dsolve/numeric/bvp) Newton iteration is...

April 08 2014
0 4

i want to find initial condition for F(0),G(0), H(0) and thetap(0) which is are missing in this problem.. then i facing this error Error, (in dsolve/numeric/bvp) Newton iteration is not converging

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/hydronew2.mw .

### Need to solve system of PDEs...

April 07 2014
2 9

Hi, everyone!

I need help.

There are a system of 2 pde's:

diff(Y(x, t), x\$2) = exp(-2*x*b)*(A(x, t)-Y(x, t)), diff(A(x, t), t) = exp(-2*x*b)*(Y(x, t)-A(x, t))

and initial and boundary conditions:

A(x, 0) = 0, Y(0, t) = 0.1, (D[1](Y))(0, t) = 0.

Goal:
For each b = 0, 0.05, 0.1.
1)to plot 3-d  Y(x,t): 0<=x<=20,0<=t<=7.
2)to plot  Y(x,4).

Are there any methods with no finite-difference mesh?

I realized the  methods such as  pds1 := pdsolve(sys, ibc, numeric, time = t, range = 0 .. 7)  can't help me:

Error, (in pdsolve/numeric/match_PDEs_BCs) cannot handle systems with multiple PDE describing the time dependence of the same dependent variable, or having no time dependence

I found something, that can solve my system analytically:
pds := pdsolve(sys), where sys - my system without initial and boundary conditions. At the end of the output: huge monster, consisted of symbols and numbers :) And I couldn't affiliate init-bound conditions to it.

I use Maple 13.

### Initial condition syntax issue...

February 28 2014
0 3

Hello everyone,

I need help to type in the following type of initial condition.

diff(1/x*diff(F(x),x),x)=0 at x =0.

Thanks

### Differential equations but with upper and lower bo...

February 03 2014
1 2

In a trivial example of where x goes from 0 to 1 of d n(x)/dx =a, where n(0)=1, n(1)=2, so that the integral is solved easily, how can i do this in maple however I can only solve an eqation with the initial condition, if i try anything else then i get errors such as,

fx := diff(n(x), x)-a

A := rhs(dsolve({fx, x = 0 .. 1, n(0) = 1, n(1) = 2}, n(x)));

Error, (in dsolve) invalid terms in sum: 0 .. 1

### Heat Equation with Robin Boundary Condition and In...

January 23 2014
0 0

I am trying to get a solution to the heat equation with multiple boundary conditions.

Most of them work but I am having trouble with two things: a Robin boundary condition and initial conditions.

First, here are my equations that work:

returns a solution (actually two including u(x,y,z,t)=0).

However, when I try to add:

or

I no longer get a solution.

Any guidance would be appreciated.

Regards.

I have uploaded a worksheet with the equations...