An Overview of Haar Wavelet Method for Solving Differential and Integral Equations

Investigation of various wavelet methods, for its capability of analyzing various dynamic phenomena through waves gained more and more attention in engineering research. Starting from ‘offering good solution to differential equations’ to capturing the nonlinearity in the data distribution, wavelets are used as appropriate tools that provide good mathematical model for scientific phenomena, which are usually modeled through linear or nonlinear differential equations. Review shows that the Haar wavelet method (HWM) is efficient and powerful in solving wide class of linear and nonlinear differential equations. The discrete wavelet transform has gained the reputation of being a very effective signal analysis tool for many practical applications. This review intends to provide the great utility of Haar wavelets to science and engineering problems which owes its origin to 1910. Besides future scope and directions involved in developing Haar wavelet algorithm for solving differential equations are addressed.