A study on solution of differential equations using Haar wavelet collocation method

Abstract

In this contest of study, problems regarding differential equations are studied when the differential equations: ordinary or partial differential equations have no solution in direct method or it is very difficult to find the required integral.When this type of problem arises, mainly numerical solution method comes to a picture. From the different numerical methods haar wavelet transform method is one to use it in solving differential equations.Before coming directly to the solution of differential equations haar wavelet function and its properties are studied. Using the properties of haar wavelet transform a useful term from the differential equation is approximated by the summation of constant multiples of the haar functions which are known functions and easy to handle. Then the other terms of the differential equations are found out by integrating or differentiating the above discussed problem. Using a logical method the differential equations are solved. And it is observed that the solution gives less error. So this method can be an efficient method.