The new modified Ishikawa iteration method for the approximate solution of different types of differential equations

Fixexd point theory and applications

Yasemin Bakr¹  Necdet Bildik¹  Ali Mutlu¹ 

[1] Department of Mathematics, Faculty of Science and Arts, Celal Bayar University, Manisa, Turkey

关键词: ordinary differential equation;    Euler method;    fixed point;    numerical analysis;    modified Ishikawa iteration;    Picard successive iteration method;   

DOI  :  10.1186/1687-1812-2013-52

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this article, the new Ishikawa iteration method is presented to find the approximate solution of an ordinary differential equation with an initial condition. Additionally, some numerical examples with initial conditions are given to show the properties of the iteration method. Furthermore, the results of absolute errors are compared with Euler, Runge-Kutta and Picard iteration methods. Finally, the present method, namely the new modified Ishikawa iteration method, is seen to be very effective and efficient in solving different type of the problem. MSC:65K15, 65L07, 65L06, 65L70.

【 授权许可】

CC BY