Homotopy Analysis Method Based on Optimal Value of the Convergence Control Parameter for Solving Semi-Differential Equations
Abstract
In this paper, homotopy analysis method is directly extended
to investigate nth order semi-differential equations and to derive
their numerical solutions which is introduced by replacing some
integer-order space derivatives by fractional derivatives. The fractional
derivatives are described in the Caputo sense. So the homotopy analysis
method for differential equations of integer-order is directly extended to
derive explicit and numerical solutions of the fractional differential equations.
An optimal value of the convergence control parameter is given
through the square residual error. Comparison is made between Homotopy
perturbation method, collocation spline method, and the present
method.
to investigate nth order semi-differential equations and to derive
their numerical solutions which is introduced by replacing some
integer-order space derivatives by fractional derivatives. The fractional
derivatives are described in the Caputo sense. So the homotopy analysis
method for differential equations of integer-order is directly extended to
derive explicit and numerical solutions of the fractional differential equations.
An optimal value of the convergence control parameter is given
through the square residual error. Comparison is made between Homotopy
perturbation method, collocation spline method, and the present
method.
Keywords
Homotopy analysis method (HAM); Caputo
fractional derivative; semi-differential equations
Refbacks
- There are currently no refbacks.
This work is licensed under a Creative Commons Attribution 3.0 License.