K. Aruna

Differential transform method for solving the linear and nonlinear Klein-Gordon equation

Abstract In this paper, we implemented relatively new, exact series method of solution known as the differential transform method for solving linear and nonlinear Klein–Gordon equation. Several illustrative examples are given to demonstrate the effectiveness of the present method.

He's variational iteration method for treating nonlinear singular boundary value problems

This paper applies Hes variational iteration method for solving nonlinear singular boundary value problems. The solution process is illustrated and various physically relevant results are obtained. Comparison of the obtained results with exact solutions shows that the method used is an effective and highly promising method for treating various classes of both linear and nonlinear singular boundary value problems.

Differential Transform – Pade Technique for Treating Non-linear Singular Boundary Value Problems Arising in the Applied Sciences

Abstract This paper applies differential transform – Pade technique for treating non-linear singular boundary value problems arising in various physical problems of science and engineering. Comparisons are made between the results of the proposed method, and the exact solutions. The results show that the proposed method is an attractive method for solving non-linear singular boundary value problems.

Variational iteration method for twelfth-order boundary-value problems

In this paper, Hes variational iteration method is applied to solve twelfth-order boundary-value problems. The numerical results obtained with minimum amount of computation are compared with the exact solutions to show the efficiency of the method. The results show that the variational iteration method is of high accuracy, more convenient and efficient for solving high-order boundary-value problems.

Solution of time fractional Black-Scholes European option pricing equation arising in financial market

Abstract In this paper, we present fractional differential transform method (FDTM) and modified fractional differential transform method (MFDTM) for the solution of time fractional Black-Scholes European option pricing equation. The method finds the solution without any discretization, transformation, or restrictive assumptions with the use of appropriate initial or boundary conditions. The efficiency and exactitude of the proposed methods are tested by means of three examples.

Solution of fractional third-order dispersive partial differential equations

Abstract In this paper, we proposed fractional differential transform method(FDTM) and modified fractional differential transform method(MFDTM) for the solution of fractional third-order dispersive partial differential equations in one- and higher-dimensional spaces. The plotted graphs illustrate the behavior of the solution for different values of fractional orderα. The efficiency and accurateness of the proposed methods are examined by means of four numerical experiments.

Computer Oriented Process for Treating Second Order Differential Equations with Singular Coefficient at the First Derivative Term

This paper applies the computer oriented process for solving second order differential equations with singular coefficient at the first derivative term. The original differential equation is modified at the singular point and then the differential equation is treated by using spline in tension. To test the efficiency of the proposed method both homogeneous and non-homogeneous singular boundary value problems are considered.