Jaime_mc2

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These are questions asked by Jaime_mc2

Hello, I'm using Maple 2021.2 to approximate the solution to a differential equation using a pseudospectral expansion in the basis of Hermite polynomials. After setting up some equations, I get a non-linear system of equations that I try to solve using the Maple's function solve, but Maple suddenly crashes during the execution of this function.

My code is the following:

HN := (n, y) -> exp(-1/2*y^2)*simplify(HermiteH(n, y))/sqrt(sqrt(Pi)*2^n*n!):

u7 := a0*HN(0, y) + a1*HN(1, y) + a2*HN(2, y) + a3*HN(3, y) + a4*HN(4, y) + a5*HN(5, y) + a6*HN(6, y):

resid := diff(u7, y $ 2) + 4*y*diff(u7, y)*u7 + 2*u7^2:

r := evalf(allvalues(RootOf(HermiteH(7, x), x)));
equations := {evalf(eval(u7, y = 0) - 1)};
for root_r in r do
    if root_r != 0 then
        equations := {op(equations), evalf(eval(resid, y = root_r))};
    end if:
end do:

solutions := solve(equations, {a0, a1, a2, a3, a4, a5, a6}):

Does anyone have any idea about what is happening? Is there any better way of solving a non-linear system of equations?

Hello everyone, I'm trying to interpolate a function using the roots of a Chebyshev polynomial as interpolation points, and then compute the absolute error. I want to compute that error via numerical integration, however, Maple is returning the expression of the integration itself. Why is that?

This is the code I'm using:

with(CurveFitting):

u := x -> exp(1/2*x^2 - 1/2):

r := evalf(allvalues(RootOf(ChebyshevT(5, x), x))):
points := Vector(5, i -> r[i]):
u_points := Vector(5, i -> u(points[i])):

P__2 := PolynomialInterpolation(points, u_points, x):

evalf(int(abs(u(x) - P__2), x = -1 .. 1))

This is the result:

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