ON APPROXIMATE AND CLOSED-FORM SOLUTION METHOD FOR INITIAL-VALUE WAVE-LIKE MODELS

This work presents a proposed Modified Differential Transform Method (MDTM) for obtaining both closed-form and approximate solutions of initial-value wave-like models with variable, and constant coefficients. Our results when compared with the exact solutions of the associated solved problems, show that the method is simple, effective and reliable. The results are very much in line with their exact forms. The method involves less computational work without neglecting accuracy. We recommend this simple proposed technique for solving both linear and nonlinear partial differential equations (PDEs) in other aspects of pure and applied sciences

Perturbation Iteration Transform Method for the Solution of Newell-Whitehead-Segel Model Equations

In this study, a computational method referred to as Perturbation Iteration Transform Method (PITM), which is a combination of the conventional Laplace Transform Method (LTM) and the Perturbation Iteration Algorithm (PIA) is applied for the solution of Newell-Whitehead- Segel Equations (NWSEs). Three unique examples are considered and the results obtained are compared with their exact solutions graphically. Also, the results agree with those obtained via other semi-analytical methods viz: New Iterative Method and Adomian Decomposition Method. This present method proves to be very efficient and reliable. Mathematica 10 is used for all the computations in this stud

The Solution of Initial-value Wave-like Models via Perturbation Iteration Transform Method

This work is based on the application of the new Perturbation Iteration Transform Method (PITM), which is a combined form of the Perturbation Iteration Algorithm (PIA) and the Laplace Transform (LT) method on some wave-like models with constant and variable coefficients. The method provides the solution in closed form, is efficient and it involves less computational work

Solving Linear Schrödinger Equation through Perturbation Iteration Transform Method

This paper applies Perturbation Iteration Transform Method: a combined form of the Perturbation Iteration Algorithm and the Laplace Transform Method to linear Schrödinger equations for approximate-analytical solutions. The results converge rapidly to the exact solution

On the Solution of the Cahn-Hilliard Equation via the Perturbation Iteration Transform Method

Recently, a new approach called the Perturbation Iteration Transform Method has been introduced. This approach is based on the fusion of the Perturbation Iteration Algorithm and the Laplace Transform Method. In this paper, the solution of the nonlinear partial differential equation: Cahn-Hilliard equation is presented by using this new scheme. Some numerical tests are presented to make apparent the potential of this new approach. The results show that the approximate solutions of these equations are very close to their exact solutions even with less computational stres

Common Fixed Point Theorems for Four Maps in G-Partial Metric Spaces

The common fixed point principle for two set of maps satisfying specified contractive conditions in cone metric spaces is proved in the context of G-partial metric space and none of the maps involved therein is continuous. Our research outcome extends well known similar results available in the literature

A Handy Approximation Technique for Closedform and Approximate Solutions of Time- Fractional Heat and Heat-Like Equations with Variable Coefficients

In this paper, we propose a handy approximation technique (HAT) for obtaining both closed-form and approximate solutions of time-fractional heat and heat-like equations with variable coefficients. The method is relatively recent, proposed via the modification of the classical Differential Transformation Method (DTM). It devises a simple scheme for solving the illustrative examples, and some similar PDEs. Besides being handy, the results obtained converge faster to their exact forms. This shows that this modified DTM (MDTM) is very efficient and reliable. It involves less computational work, even without given up accuracy. Therefore, we strongly recommend it for solving both linear and nonlinear time-fractional partial differential equations (PDEs) with applications in other aspects of pure and applied sciences, management, and finance

Adomian decomposition method for analytical solution of a continuous arithmetic Asian option pricing model

One of the main issues of concern in financial mathematics has been a viable method for obtaining analytical solutions of the Black-Scholes model associated with Arithmetic Asian Option (AAO). In this paper, a proposed semi-analytical technique: Adomian Decomposition Method (ADM) is applied for the first time, for analytical solution of a continuous arithmetic Asian option model. The ADM gives the solution in explicit form with few iterations. The computational work involved is less. However, high level of accuracy is not neglected. The obtained solution conforms with those of Rogers and Shi (J. of Applied Probability 32: 1995, 1077-1088), and Elshegmani and Ahmad (ScienceAsia, 39S: 2013, 67–69). Thus, the proposed method is highly recommended for analytical solution of other versions of Asian option pricing models such as the geometric form for puts and calls, even in their time-fractional forms

Local Fractional Operator for the Solution of Quadratic Riccati Differential Equation with Constant Coefficients

In this paper, we consider approximate solutions of fractional Riccati differential equations via the application of local fractional operator in the sense of Caputo derivative. The proposed semi-analytical technique is built on the basis of the standard Differential Transform Method (DTM). Some illustrative examples are given to demonstrate the effectiveness and robustness of the proposed technique; the approximate solutions are provided in the form of convergent series. This shows that the solution technique is very efficient, and reliable; as it does not require much computational work, even without given up accuracy