𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Numerical solution of differential equations using Haar wavelets

✍ Scribed by Ü. Lepik

Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
181 KB
Volume
68
Category
Article
ISSN
0378-4754

No coin nor oath required. For personal study only.

✦ Synopsis

Haar wavelet techniques for the solution of ODE and PDE is discussed. Based on the Chen-Hsiao method [C.F. Chen, C.H. Hsiao, Haar wavelet method for solving lumped and distributed-parameter systems, IEE Proc.-Control Theory Appl. 144 (1997) 87-94; C.F. Chen, C.H. Hsiao, Wavelet approach to optimising dynamic systems, IEE Proc. Control Theory Appl. 146 (1997) 213-219] a new approach-the segmentation method-is developed. Five test problems are solved. The results are compared with the result obtained by the Chen-Hsiao method and with the method of piecewise constant approximation [

📜 SIMILAR VOLUMES

Numerical solution of nonlinear Fredholm
Numerical solution of nonlinear Fredholm integral equations of the second kind using Haar wavelets
✍ E. Babolian; A. Shahsavaran 📂 Article 📅 2009 🏛 Elsevier Science 🌐 English ⚖ 418 KB

In this work, we present a computational method for solving nonlinear Fredholm integral equations of the second kind which is based on the use of Haar wavelets. Error analysis is worked out that shows efficiency of the method. Finally, we also give some numerical examples.

Numerical solution of nth-order integro-
Numerical solution of nth-order integro-differential equations using trigonometric wavelets
✍ Mehrdad Lakestani; Mahmood Jokar; Mehdi Dehghan 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 219 KB

The main aim of this paper is to apply the trigonometric wavelets for the solution of the Fredholm integro-differential equations of nth-order. The operational matrices of derivative for trigonometric scaling functions and wavelets are presented and are utilized to reduce the solution of the Fredhol

Application of the Haar functions to sol
Application of the Haar functions to solution of differential equations
✍ Masaaki Ohkita; Yasuhiro Kobayashi; Michio Inoue 📂 Article 📅 1983 🏛 Elsevier Science 🌐 English ⚖ 446 KB

In this paper, it is proposed that Haar functions should be used for solving ordinary differential equations of a time variable in facilitv. This is because inteorated forms of Haar functions of any degree can be illustrated by linear-and linear segmentfunctions like as triangles. Fortunately, sinc

NUMERICAL SOLUTION OF THE STATIONARY FPK
NUMERICAL SOLUTION OF THE STATIONARY FPK EQUATION USING SHANNON WAVELETS
✍ S. MCWILLIAM; D.J. KNAPPETT; C.H.J. FOX 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 448 KB

The Fokker}Planck}Kolmogorov (FPK) equation governs the probability density function (p.d.f.) of the dynamic response of a particular class of linear or non-linear system to random excitation. This paper proposes a numerical method for calculating the stationary solution of the FPK equation, which i