# SIMPLICIAL HOMOTOPY METHOD FOR THE SOLUTION OF NONLINEAR TWO-POINT BOUNDARY VALUE PROBLEMS.

Kiyotaka Yamamura, Shinichi Oishi, Kazuo Horiuchi

Research output: Contribution to journalArticle

### Abstract

This paper proposes an efficient numerical method for the solution of nonlinear two-point boundary value problems, based on the simplicial homotopy method and the decomposition technique. It is shown first that the system of equations to consider can always be reduced to the system of equations with lower dimension, by applying the decomposition technique to the system of finite difference equations. An efficient mesh refinement strategy is proposed, taking into consideration the accuracy of the simplicial approximation.

Original language English 40-48 9 Electronics and Communications in Japan, Part I: Communications (English translation of Denshi Tsushin Gakkai Ronbunshi) 68 11 Published - 1985 Nov

### Fingerprint

Boundary value problems
Decomposition
Difference equations
Numerical methods

### ASJC Scopus subject areas

• Computer Networks and Communications
• Electrical and Electronic Engineering

### Cite this

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title = "SIMPLICIAL HOMOTOPY METHOD FOR THE SOLUTION OF NONLINEAR TWO-POINT BOUNDARY VALUE PROBLEMS.",
abstract = "This paper proposes an efficient numerical method for the solution of nonlinear two-point boundary value problems, based on the simplicial homotopy method and the decomposition technique. It is shown first that the system of equations to consider can always be reduced to the system of equations with lower dimension, by applying the decomposition technique to the system of finite difference equations. An efficient mesh refinement strategy is proposed, taking into consideration the accuracy of the simplicial approximation.",
author = "Kiyotaka Yamamura and Shinichi Oishi and Kazuo Horiuchi",
year = "1985",
month = "11",
language = "English",
volume = "68",
pages = "40--48",
journal = "Electronics and Communications in Japan, Part I: Communications (English translation of Denshi Tsushin Gakkai Ronbunshi)",
issn = "8756-6621",
publisher = "John Wiley and Sons Inc.",
number = "11",

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AU - Yamamura, Kiyotaka

AU - Oishi, Shinichi

AU - Horiuchi, Kazuo

PY - 1985/11

Y1 - 1985/11

N2 - This paper proposes an efficient numerical method for the solution of nonlinear two-point boundary value problems, based on the simplicial homotopy method and the decomposition technique. It is shown first that the system of equations to consider can always be reduced to the system of equations with lower dimension, by applying the decomposition technique to the system of finite difference equations. An efficient mesh refinement strategy is proposed, taking into consideration the accuracy of the simplicial approximation.

AB - This paper proposes an efficient numerical method for the solution of nonlinear two-point boundary value problems, based on the simplicial homotopy method and the decomposition technique. It is shown first that the system of equations to consider can always be reduced to the system of equations with lower dimension, by applying the decomposition technique to the system of finite difference equations. An efficient mesh refinement strategy is proposed, taking into consideration the accuracy of the simplicial approximation.

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EP - 48

JO - Electronics and Communications in Japan, Part I: Communications (English translation of Denshi Tsushin Gakkai Ronbunshi)

JF - Electronics and Communications in Japan, Part I: Communications (English translation of Denshi Tsushin Gakkai Ronbunshi)

SN - 8756-6621

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ER -