## how do i solve the boundary conditions...

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I found the solution of P(r) at P(0)=0, but could obtain the result of v(r) at v(1014030)=-0.4283, v(r) may have a graph such that i can goes from -0.4283 to 0.

## Error, (in fproc) unable to store 'HFloat(1.043007...

Please anyone, I have been battling with this problem for a while yet the error message keeps coming. Would be happy if responded to.

Thanks

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## How to calculate this integral with Maple?...

Let us consider the improper integral

int((abs(sin(2*x))-abs(sin(x)))/x, x = 0 .. infinity);

Si(Pi)-Si((1/2)*Pi)+sum(-(-1)^_k*Si(Pi*_k)+signum(sin((1/2)*Pi*_k))*Si((1/2)*Pi*_k)+Si(Pi*_k+Pi)*(-1)^_k-signum(cos((1/2)*Pi*_k))*Si((1/2)*Pi*_k+(1/2)*Pi), _k = 1 .. infinity)


Mathematica 11 produces a similar expression and a warning

Integrate::isub: Warning: infinite subdivision of the integration domain has been used in computation of the definite integral \!$$\*SubsuperscriptBox[\(\[Integral]$$, $$0$$, $$\[Infinity]$$]$$\*FractionBox[\(\(-Abs[Sin[x]]$$ + Abs[Sin[2\ x]]\), $$x$$] \[DifferentialD]x\)\). If the integral is not absolutely convergent, the result may be incorrect.

Up to Pedro Tamaroff http://math.stackexchange.com/questions/61828/proof-of-frullanis-theorem , the answer is 2/Pi*ln(2) because of

J := int(abs(sin(2*x))-abs(sin(x)), x = 0 .. T) assuming T>2;
-1/2-signum(sin(T))*signum(cos(T))*cos(T)^2+(1/2)*signum(sin(T))*signum(cos(T))+cos(T)*signum(sin(T))+floor(2*T/Pi)

B := limit(J/T, T = infinity);
2 /Pi

K := x*(int((abs(sin(2*t))-abs(sin(t)))/t^2, t = x .. 1)) assuming x>0,x<1;

2*sin(x)*cos(x)-2*Ci(2*x)*x+Ci(x)*x+sin(1)*x-sin(2)*x+2*Ci(2)*x-Ci(1)*x-sin(x)

A := limit(K, x = 0, right);
0


Its numeric calculation results

evalf(Int((abs(sin(2*x))-abs(sin(x)))/x, x = 0 .. infinity));
Float(undefined)


which seems not to be true.

The question is: how to obtain the reliable results for it with Maple, both symbolic and numeric?

## i need a help in solving the assignment...

I faced difficulity in solving this problem. Can you help

Consider the expression

Build a function to calculate an approximation for the value of the given expression for
any value for B

## Fourier Transforms...

Dear all,

I need to transforme these equation from time domain to frequency domain with fourier transforms and solve it in frequency domain but i received the flowing error

any helps

thank you !

 > restart:with(inttrans):
 > E:=1;L:=1;
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 > eq:=fourier(equ,t,omega);
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Code :

## Solution of system of nonlinear algebraic equation...

Dears;

Hope everyone is fine. I am try to find the numerical solutions of system of nonlinear algabric equation via newton's raphson method in the attached file but failed. Please see the attachment and try to correct. You can solve it least square method if possible. I am waiting your positive response.

Help_in_Newton.mw

With my best regards and sincerely.

School of Mathematical Sciences
Peking University, Beijing, China

## 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