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Application of the Haar functions to solution of differential equations

Author

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  • Ohkita, Masaaki
  • Kobayashi, Yasuhiro
  • Inoue, Michio

Abstract

In this paper, it is proposed that Haar functions should be used for solving ordinary differential equations of a time variable in facility. This is because integrated forms of Haar functions of any degree can be illustrated by linear- and linear segment-functions like as triangles. Fortunately, since they are placed where Haar functions are defined in a specified form respectively, these functions are computable by algebraic operations of quasi binary numbers. Therefore, when a given function is approximated in a form of stairsteps on a Haar function system their integration can be termwise executed by shift and add operations of coefficients of the approximation. The use of this system is comparable with an application using the midpoint rule in numerical integration. In this line, nonlinear differential equations can be solved like as linear differential equations.

Suggested Citation

  • Ohkita, Masaaki & Kobayashi, Yasuhiro & Inoue, Michio, 1983. "Application of the Haar functions to solution of differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 25(1), pages 31-38.
    • Handle: RePEc:eee:matcom:v:25:y:1983:i:1:p:31-38
    DOI: 10.1016/0378-4754(83)90027-7
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    Cited by:

    1. Ohkita, Masaaki & Kobayashi, Yasuhiro, 1988. "An application of rationalized Haar functions to solution of linear partial differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 30(5), pages 419-428.
    2. Ohkita, Masaaki, 1985. "Evaluation of analytic functions by generalized digital integration," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 27(5), pages 511-517.

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