# Solution of a polylocal problem with a pseudospectral method

## Abstract

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.

## Authors

Ion Păvăloiu

Daniel N. Pop (Sibiu)

Radu T. Trimbitas (Cluj-Napoca)

Ion Pavaloiu (Cluj-Napoca)

## Keywords

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

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

## PDF

##### Cite this paper as:
D.N. Pop, R.T. Trîmbiţaş, I. Păvăloiu, Solution of a polylocal problem with a pseudospectral methodAnnals of the Tiberiu Popoviciu Seminar of Functional Equations, Approximation and Convexity8 (2010), pp. 53-64

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.

##### DOI

Not available yet.

1584-4536

##### Online ISSN

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