TY - JOUR
ID - 13106
TI - A three step superconvergent algorithm for the solution of generalized Burgers’-Huxley and Burgers’-Fisher equations
JO - Journal of Advanced Mathematical Modeling
JA - JAMM
LA - en
SN - 2251-8088
AU - Ghasemi, Mohammad
AD - Department of Mathematics, University of Kurdistan, Sanandaj, Iran
Y1 - 2017
PY - 2017
VL - 7
IS - 1
SP - 117
EP - 137
KW - Spline
KW - Superconvergence approximations
KW - Burgers’-Huxley equation
KW - Burgers’-Fisher equation
KW - Green’s function
KW - Convergence
DO - 10.22055/jamm.2017.13106
N2 - 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.
UR - https://jamm.scu.ac.ir/article_13106.html
L1 - https://jamm.scu.ac.ir/article_13106_7d6aad480bc2c184fe6b005847d0e802.pdf
ER -