## Jaggered graph for fdiff function...

For my fdiff graph, it seems that the cirtical points appear to be jaggered or not smooth. Anyone nows what seem to be the problem? i tried increasing the numpoints but it did not work:( I am open to all opinions. Thanks:)

fyp2.mw

## Error, Initial newton iteration is not converging...

For the ODE system with boundary conditions, I was able to obtain solutions for n=0, but not for n>0. I obtained the error, Initial newton iteration is not converging. Anyone knows the solution for this? I am open to all suggestions and any help would be greatly appreciated:)

ODE_solution.mw

## Error, (in dsolve/numeric/bvp/convertsys) too few ...

If i have boundary conditions with D(psi), i have no problem. But if i have condition with psi(infinity) (which i need), Maple says "too few boundary conditions". Maybe i make stupid mistakes, but i don't see.

restart;
assume(r, nonnegative);
ic_Re := &psi;Re(0) = 0, (D(&psi;Re))(0) = 0;
ic_Im := &psi;Im(0) = 0, (D(&psi;Im))(0) = 0;
V0 := 2.5; ERe := 1.5; EIm := 1.2; &hbar; := 6.582; mu := 938.27*(1/2); Q0 := 1.5; Rq := 4.5; Rv := 2.5;
Q := proc (r) options operator, arrow; -Q0*exp(-r/Rq) end proc;
V := proc (r) options operator, arrow; -V0*exp(-r/Rv) end proc;
Eqn_&psi;Re := -&hbar;^2*(diff(&psi;Re(r), r, r)+2*(diff(&psi;Re(r), r))/r)/(2*mu)-ERe*&psi;Re(r)+V(r)+EIm*&psi;Re(r) = Q(r);
Eqn_&psi;Im := -&hbar;^2*(diff(&psi;Im(r), r, r)+2*(diff(&psi;Im(r), r))/r)/(2*mu)-EIm*&psi;Re(r)-ERe*&psi;Im(r) = 0;
F := dsolve({ic_Im, ic_Re, Eqn_&psi;Im, Eqn_&psi;Re}, numeric);
plots[odeplot](F, [r, &psi;Re(r)], r = 0 .. 20, numpoints = 500);

plots[odeplot](F, [r, &psi;Re(r)], r = 0 .. 20, numpoints = 500);

restart;
assume(r, nonnegative);
ic_Re := &psi;Re(0) = 0, &psi;Re(infinity) = 0;
ic_Im := &psi;Im(0) = 0, &psi;Im(infinity) = 0;
V0 := 2.5; ERe := 1.5; EIm := 1.2; &hbar; := 6.582; mu := 938.27*(1/2); Q0 := 1.5; Rq := 4.5; Rv := 2.5;
Q := proc (r) options operator, arrow; -Q0*exp(-r/Rq) end proc;
V := proc (r) options operator, arrow; -V0*exp(-r/Rv) end proc;
Eqn_&psi;Re := -&hbar;^2*(diff(&psi;Re(r), r, r)+2*(diff(&psi;Re(r), r))/r)/(2*mu)-ERe*&psi;Re(r)+V(r)+EIm*&psi;Re(r) = Q(r);
Eqn_&psi;Im := -&hbar;^2*(diff(&psi;Im(r), r, r)+2*(diff(&psi;Im(r), r))/r)/(2*mu)-EIm*&psi;Re(r)-ERe*&psi;Im(r) = 0;
F := dsolve({ic_Im, ic_Re, Eqn_&psi;Im, Eqn_&psi;Re}, numeric);
Error, (in dsolve/numeric/bvp/convertsys) too few boundary conditions: expected 5, got 4

## Plotting wavefunctions...

Hi, I have been trying to solve the Schrodinger equation for harmonic oscillators using dsolve and plot the the wavefunctions for the different energy levels. However I am struggling to plot all the different wavefuntions on the same plot. I also want to normalize the wavefunctions to help compare their shapes and values. Here's my code:- schro := {diff(psi(x), x, x)-(alpha*x^4+x^2-energy)*psi(x) = 0}; // d / d \\ / 4 2 \ \ { |--- |--- psi(x)|| - \alpha x + x - energy/ psi(x) = 0 } \\ dx \ dx // / ic := {psi(3) = 0, (D(psi))(3) = 1}; {psi(3) = 0, D(psi)(3) = 1} schro1 := subs(energy = 3.30687, alpha = .1, schro); soln1 := dsolve(schro1 union ic, {psi(x)}, type = numeric); // d / d \\ / 4 2 \ \ { |--- |--- psi(x)|| - \0.1 x + x - 3.30687/ psi(x) = 0 } \\ dx \ dx // / proc(x_rkf45) ... end; with(plots); [animate, animate3d, animatecurve, arrow, changecoords, complexplot, complexplot3d, conformal, conformal3d, contourplot, contourplot3d, coordplot, coordplot3d, densityplot, display, dualaxisplot, fieldplot, fieldplot3d, gradplot, gradplot3d, implicitplot, implicitplot3d, inequal, interactive, interactiveparams, intersectplot, listcontplot, listcontplot3d, listdensityplot, listplot, listplot3d, loglogplot, logplot, matrixplot, multiple, odeplot, pareto, plotcompare, pointplot, pointplot3d, polarplot, polygonplot, polygonplot3d, polyhedra_supported, polyhedraplot, rootlocus, semilogplot, setcolors, setoptions, setoptions3d, shadebetween, spacecurve, sparsematrixplot, surfdata, textplot, textplot3d, tubeplot] odeplot(soln1, [x, psi(x)], -3 .. 3); Thank in advance

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

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

 (1)

 (2)

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

thanks...

## How to solve numerically a Fredholm integral equat...

Hi guys,

I am trying to solve a Fredholm equation of the second kind using Maple. An analytical expression cannot be in principle found. I was wondering whether Maple does numerical evaluation of such integral equations. Please see the equation in attach. Any help is highly appreciated.

Thanks

F

Question.mw

## Den Iseger algorithm for numerical Laplace transfo...

Dear Community,

Would someone have a good and easy to understand/implement description of the Den Iseger algorithm for the numerical inversion of Laplace transform? Even better if someone would have a Maple script to do it, that would be superb.

best regards

Andras

## Error, (in dsolve/numeric/bvp) singularity encount...

Hi

may every one help to me for dsolve this differentia1l equation?

error:

Error, (in dsolve/numeric/bvp) singularity encountered

Turbulent2-kw.mw

## Numerical integration speed in Maple 18 vs. 2015...

I have recently acquired Maple 2016 and wanted to see how its numerical integration compared to previous version (in this instance, 2015 and 18). This integration is a tougher problem than the usual "textbook" case using a well behaved function. The integrand presented in the worksheet below is a small example but it can get much larger.

I am calculating a triple integral numerically from a function read in from a file which contains Laguerre polynomials. Some simplifications are done first and then that is fed into the integration. In the example script below the input has been put into the program to make it simpler.

So far it appears Maple 18 is faster than 2015 (in this case anyway) and 2016 does not appear to like the syntax I am using even though it runs fine on 18 and 2015 (it does not like the simplify(expr1,LaguerreL) or sqrt parts).

Looking at the stats of the calculation runs:

Maple 18:

memory used=0.52MiB, alloc change=0 bytes, cpu time=20.33s, real time=20.49s, gc time=0ns

Maple 2015:

memory used=350.84KiB, alloc change=0 bytes, cpu time=28.77s, real time=29.24s, gc time=0ns

What is interesting is that Maple 18 is allocating more memory in order to solve the problem compared to 2015. Does anyone have any ideas why this is occuring? Also has there been a syntax change from 2015 -> 2016 which I have not been aware of. Is there a different way to write the script to run in 2016?

Here is the worksheet:

Maple_numeric_speed.mw

- Yeti

## Finite Difference Method for PDE...

Dear all

I have a PDE and its analytical solution. I want to find the numerical solution by Finite Difference Method.

I duscratize the PDE and boundary condition and Could not able to solve them togethe.

Here is the file FEM-Nu.mw

## how pdsolve time-fractional equation in maple?...

hi...how i can pdsolve this equation numerically or analyticlly?

this equation is time-fractional  equation with generalized Cattaneo model

where

is the fractional derivative operator considered in the
Caputo sense.

FRACTION.mw

 (1)

 (2)

 (3)

Hello everybody!

Please help me to solve the attached partial differential equation. I am getting an error. I do have its analytical solution and that works fine.

The error is as follows
Error, (in pdsolve/numeric/plot) unable to compute solution for t>HFloat(0.0):
solution becomes undefined, problem may be ill posed or method may be ill suited to solution

The worksheet is attached hereshortsngle.mw

## Error for (in EpResult) ...

what does this mean:"Error, (in EpResult) cannot evaluate the solution further right of 0.36919453e-2, probably a singularity" as I cannot find any relevant material of this error.

I am simulating a condition and get to the final stage of calculation, and this error occurs....

## Numerical solution of a function...

Hi,

This is regarding numerical solution of a function and plot. I have a function in the form of , and i need to plot it with omega (as the expression is too long i cant insert it here). Now, if i am changing the range of omega in plot command then I am getting different plots for the small values of omega. Let's say if i change the range from 1..10 to 1..50 and look at the plot in the range of 1..3 then the plots looks different. Apart from this if i change the value of Digits  from 10 to 30 or 40 then every time i am getting an entire different  plot. As the expression if too long i cant convert it to Matlab expression and plot there. How to fix these issues. Please help me regarding this.

Regarding

Sunit

## 2D Grid Interpolation...

Hi,

I'm solving a 2D grid with some finite-diference methods. The result is a surface, i.e f(x,y) = z. Where X and Y and points on a grid.

I then need to integrate over this grid, i.e

int(f(x,y),[x=0..10, y=0..10])

I have tried interpolating the grid. I've used CurveFitting:-ArrayInterpolation() to interpolate points in this 2D space and then integrate over them.

I'm using a 30x30 grid, but this interpolation scheme takes far too long. The function generated from the ArrayInterpolation creates an interpolation every time a point is evaluated, which I assume is why the integral is very computationally expensive.

I would like to create a piecewise analytic function from the 2-D grid, perhaps using CurveFitting:-Spline(), however from my understanding this only works for 1D objects?

Is there any better solution for integrating a 2D numeric grid?