An application of rationalized Haar functions to solution of linear partial differential equations. (English) Zbl 0659.65109

Based on previous articles of the authors, the rational Haar functions method is applied for solving first and second-order partial differential equations. New operational matrices of both integration and differentiation based on double rationalized Haar series is derived. Upon using these operational matrices for their solution, the partial differential equations are tranformed into matrix equations. Coefficients of double rationalized Haar series related to their solutions can be obtained by solving matrix equations. Numerical examples are presented.
Reviewer: V.A.Kostova


65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
35F15 Boundary value problems for linear first-order PDEs
35G15 Boundary value problems for linear higher-order PDEs
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[1] Beauchamp, K. G., (Walsh Functions and Their Applications (1975), Academic Press: Academic Press New York), 72-86 · Zbl 0326.42007
[2] Iizuka, M.; Kuno, A.; Takayama, T., Gray level transform of digital image data and bilevel display of continuous tone image, Trans. IEE Japan, 103-C, 4, 93-100 (1983)
[3] Kobayashi, Y.; Ohkita, M., Approximation of the solutions of ordinary differential equations by integrals of Haar functions, Trans. IEE Japan, 106-C, 11, 233-240 (1986)
[4] Kurosawa, Y.; Iijima, T., A new bilevel display technique of continuous tone pictures based on Haar transform, Trans. Inform. Process. Soc. Japan, 20, 3, 218-224 (1979)
[5] Ohkita, M., Evaluation of analytic functions by generalized digital integration, Math. & Comput. Simulation (Special Issue on Orthogonal Expansions and Transforms in Computation, Signal Processing and System Design), 27, 5 & 6, 511-517 (1985) · Zbl 0578.65088
[6] Ohkita, M., Haar approximation of analytic functions and its generation, Trans. IEE Japan, 105-C, 5, 101-108 (1985)
[7] Ohkita, M., An application of rationalized Haar functions to the solution of delay-differentail systems, Math. & Comput. Simulation, 29, 6, 477-491 (1987) · Zbl 0632.65093
[8] Ohkita, M.; Kobayashi, Y., An application of rationalized Haar functions to solution of linear differential equations, IEEE Trans. Circuits & Systems, CAS-33, 9, 853-862 (1986) · Zbl 0613.65072
[9] Ohkita, M.; Kobayashi, Y., An application of rationalized Haar functions to solution of time-varying linear delay systems, Proc. 12th IMACS World Congress on Scientific Computation (July 18-22, 1988), to appear
[10] Ohkita, M.; Kobayashi, Y.; Inoue, M., Application of Haar functions to solution of differential equations, Math. & Comput. Simulation, 25, 1, 31-38 (1983) · Zbl 0508.65037
[11] Shih, Y. P.; Han, J. Y., Double Walsh series solution of first-order partial differential equations, Internat. J. System Sci., 9, 569-578 (1978) · Zbl 0385.65054
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