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An Optimal Algorithm for Certain Boundary Value Problem

K. Stys
T. Stys
Journal / Anthology

Journal of Computational and Applied Mathematics
Year: 1997
Volume: 83
Page range: 195-203

The O(h^4) finite-difference scheme for the second derivative u^n(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.

*Mathematics > Calculus and Analysis > Differential Equations