Bernoulli collocation method based on residual error analysis and application to partial differential equations

This thesis consists of six chapters. In the first chapter, the historical development and literature of partial differential equations are presented. In the second chapter, basic concepts and definitions of partial differantial equations are mentioned. Also the historical development and some features of Bernoulli polynomials are given. In the third chapter, Bernoulli collocation method is intruduced to obtain the second order linear partial differential equations. In the fourth chapter, the error analysis based on residual function is developed to demonstrate the accuracy of Bernoulli collocation method. In the fifth chapter, Bernoulli collocation method and residual error analysis are applied to various model of partial differential equations. The table value and figures of the obtained solutions are given and compared each other. In the sixth chapter, the results of the study are interpreted and related for future works are also suggested.