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- Title
Approximation methods for second order nonlinear polylocal problems.
- Authors
Pop, Daniel N.; Trîmbiţaş, Radu T.
- Abstract
Consider the problem: y′ (x) + f(x, y) = 0, x ε [0, 1] y(a) = α y(b) = β, a, b ε (0, 1). This is not a two-point boundary value problem since a, b 2 (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 two solution procedures: one based on B-splines of order k + 2 and the other based on a combination of B-splines (order k + 2) with a (k + 1)- order Runge-Kutta method. Then, we give two numerical examples and compare the methods experimentally.
- Subjects
APPROXIMATION theory; NONLINEAR theories; BOUNDARY value problems; INITIAL value problems; RUNGE-Kutta formulas; NEWTON-Raphson method; SPARSE matrices
- Publication
Studia Universitatis Babeş-Bolyai, Mathematica, 2011, Vol 56, Issue 2, p515
- ISSN
0252-1938
- Publication type
Article