69 research outputs found
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
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
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
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
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