Shahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80887120170823A three step superconvergent algorithm for the solution of generalized Burgers’-Huxley and Burgers’-Fisher equationsA three step superconvergent algorithm for the solution of generalized Burgers’-Huxley and Burgers’-Fisher equations1171371310610.22055/jamm.2017.13106FAMohammadGhasemiDepartment of Mathematics, University of Kurdistan, Sanandaj, IranJournal Article20161229In this paper, a new three-step method based on cubic spline will be construct to the numerical solution of a class of partial differential equations well-known as Burgers’-Huxley and Burgers’-Fisher. As we know, the maximum order achieved using cubic spline for interpolating is , but this order is reduced when it is used for the solution of differential equations. Here we will find an superconvergent approximation for the solution of Burgers’-Huxley and Burgers’-Fisher equations by defining some proper end conditions and constructing a three step deferred-correction algorithm. We will discuss the convergence and error bounds of the method using Green’s function definition in details. In addition, to verify the obtained error bounds, some numerical examples will be presented. Finally, we will try to show the applicability and efficiency of the method by comparing the results with other existing methods.In this paper, a new three-step method based on cubic spline will be construct to the numerical solution of a class of partial differential equations well-known as Burgers’-Huxley and Burgers’-Fisher. As we know, the maximum order achieved using cubic spline for interpolating is , but this order is reduced when it is used for the solution of differential equations. Here we will find an superconvergent approximation for the solution of Burgers’-Huxley and Burgers’-Fisher equations by defining some proper end conditions and constructing a three step deferred-correction algorithm. We will discuss the convergence and error bounds of the method using Green’s function definition in details. In addition, to verify the obtained error bounds, some numerical examples will be presented. Finally, we will try to show the applicability and efficiency of the method by comparing the results with other existing methods.https://jamm.scu.ac.ir/article_13106_7d6aad480bc2c184fe6b005847d0e802.pdf