Heinrich

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9 years, 107 days
Germany

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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

Dear all,

 

I am trying to plot in the same graph two sets of data points given by vectors. Please see the example below. Any help will be highly appreciated. Thanks!

 

question.mw

Dear all,

I would like to evaluate mathematical quantities involving 3F2. The function hypergeom in Maple is most probably the so called ordinary hypergeometric function commonly denoted as 2F1.


I was wondering whether 3F2 has already been implemented in Maple. Thank you.

Dear all,

I would like to compute numerically using Maple the following improper integral

``

Integrand := (1/4)*(((((6*I)*beta-3-6*C+(6*I)*C*beta)*s^4+((24*I)*C*beta-24*C-12)*s^2+(24*I)*(1+C)*beta)*BesselK(0, s)+12*BesselK(1, s)*(C+1/2)*s^3)*BesselI(1, s)^3+6*BesselI(0, s)*(-(2*(I*beta*C*s^2+(2*I)*beta*C+(2*I)*beta+4*C+2))*s*BesselK(0, s)+((I*beta*C+I*beta-C-1/2)*s^4+((4*I)*C*beta+4*C+2)*s^2+(4*I)*(1+C)*beta)*BesselK(1, s))*BesselI(1, s)^2-(12*(-(1/2*((C+1/2)*s^2+I*beta*C+I*beta+8*C+4))*s*BesselK(0, s)+((I*beta*C+2*C+1)*s^2+(2*I)*(1+C)*beta)*BesselK(1, s)))*s*BesselI(0, s)^2*BesselI(1, s)+6*s^2*((-2*C-1)*s*BesselK(0, s)+BesselK(1, s)*((C+1/2)*s^2+I*(1+C)*beta))*BesselI(0, s)^3)/((BesselI(0, s)^2*s-BesselI(1, s)^2*s-2*BesselI(1, s)*BesselI(0, s))^2*(C+1/2)*s*Pi):

``


However, Maple does seem to give a result for this integral. I have tried to compute from e.g. 0.001 as an approximation but it turns out that the integrand diverges as s goes to zero. I have also tried some options such as method = _d01amc but I get Error, (in evalf/int) powering may produce overflow.

 

I would appreciate it if someone here could provide with some help with regards to the computation of such improper integrals. Thank you.

 

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Dear all,

I am using Maple to perform numerical integrations. When the final index in the loop is set to 5, the computation is fast and the results are quickly delivered. When I set a number higher than that, even 6, the program gets really slow and often crashes.

I herewith attach the script I use to generate the results. I guess that there should be a problem of memory management and I tried to use gc() as suggested in some forms but without success. I would appreciate it if someone here could explain the reason behind the problem.

Thank you,
question.mw

restart; Ts := 1.; sigma := 1.; C := 1.; B := 2./(1+C); with(inttrans); beta := B*Ts*omega; assume(Tb > 0); assume(u >= 0); FzzS := -(3/2)*u^3*((2*u+I*beta)*(exp(2*sigma*u)+sigma^2*exp(2*u))-4*sigma*u*((1+sigma)*u-1))/((2*u+I*beta)^2*exp((2*(1+sigma))*u)-4*u^2*((1+sigma)*u-1)^2); InvFzzS := simplify(invfourier(FzzS, omega, t)); logTimeMin := -2; logTimeMax := -1; NumSteps := 6; logTimeStep := evalf(1.0*(logTimeMax-logTimeMin)/NumSteps); curdirectory(); A := matrix(NumSteps, 2); T1 := Array(1 .. NumSteps); AF := Array(1 .. NumSteps); for i to NumSteps do logTime := evalf(i*logTimeStep+logTimeMin); curTime := evalf(10^logTime); A[i, 1] := curTime; A[i, 2] := evalf(Int(eval(InvFzzS, t = curTime), u = 0 .. infinity, epsilon = 10^(-5))); T1[i] := A[i, 1]; AF[i] := A[i, 2] end do

 

 

``

 

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