A new analytical technique to solve Fredholm's integral equations

作者：Abba**andy Saeid^*; Shivanian E

来源：Numerical Algorithms, 2011, 56(1): 27-43.

DOI：10.1007/s11075-010-9372-2

• Homotopy analysis method
• Convergence-controller parameter
• Linear and nonlinear Fredholm integral equation
• Adomian decomposition method

This paper shows that the homotopy analysis method, the well-known method to solve ODEs and PDEs, can be applied as well as to solve linear and nonlinear integral equations with high accuracy. Comparison of the present method with Adomian decomposition method (ADM), which is well-known in solving integral equations, reveals that the ADM is only special case of the present method. Also, some linear and nonlinear examples are presented to show high efficiency and illustrate the steps of the problem resolution.

• 出版日期2011-1