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An optimal algorithm for certain boundary value problem

✍ Scribed by Krystyna Styś; Tadeusz Styś

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
342 KB
Volume
83
Category
Article
ISSN
0377-0427

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✦ Synopsis

The O(h 4) finite-difference scheme for the second derivative u"(x) leads to a coherent pentadiagonal matrix which is factorized into two tridiagonal matrices. This factorization is used to derive an optimal algorithm for solving a linear system of equations with the pentadiagonal matrix. As an application, a nonlinear system of ordinary differential equations is approximated by an O(h 4) convergent finite-difference scheme. This scheme is solved by the implicit iterative method applying the algorithm at each iteration. A Mathematica module designed for the purpose of testing and using the method is attached.

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