Solution of a polylocal problem with a pseudospectral method

Consider the problem:

$$y”(x) + f(x, y) = 0, \ \ x \in [0, 1], y(a) = \alpha, y(b) = \beta, a, b ∈ (0, 1),$$

which is not a two-point boundary value problem since \(a, b ∈ (0, 1)\).

It is possible to solve this problem by dividing it into the three problems: a two-point boundary value problem (BVP) on \([a, b]\) and two initial value problems (IVP), on \([0, a]\) and \([b, 1]\).

The aim of this work is to present a solution procedure based on pseudospectral collocation with Chebyshev extreme points combined with a Runge-Kutta method. Finally, some numerical examples are given.

Daniel N. Pop
(Sibiu)

Radu T. Trimbitas
(Cluj-Napoca)

Ion Pavaloiu
(Tiberiu Popoviciu Institute of Numerical Analysis)

spectral methods; boundary-value problem; collocation; centrosymmetric matrix

Scanned paper.

Latex version of the paper.

D.N. Pop, R.T. Trimbitas, I. Pavaloiu, Solution of a polylocal problem with a pseudospectral method, Annals of the Tiberiu Popoviciu Seminar of Functional Equations, Approximation and Convexity, 8 (2010), pp. 53–63.

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