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

On a Modified Iterative Method for the Solutions of Advection Model

Variational Iterative Method (VIM) has been reported in literature as a powerful semi-analytical method for solving linear and nonlinear differential equations; however, it has also been shown to have some weaknesses such as calculation of unneeded terms, and time-consumption regarding repeated calculations for series solution. In this work, a modified VIM is applied for approximate-analytical solution of homogeneous advection model. The result attest to the robustness and efficiency of the proposed method (MVIM)

SHIFTED LEGENDRE POLYNOMIAL BASED GALERKIN AND COLLOCATION METHODS FOR SOLVING FRACTIONAL ORDER DELAY DIFFERENTIAL EQUATIONS

In this article, effective numerical methods for the solution of fractional order delay differential equations (FODDEs) are presented. The fractional derivative (FD) is defined in Caputo sense. Shifted Legendre polynomials are used in the Collocation and Galerkin methods to convert FDDEs to the linear and/or nonlinear system in algebraic form of equations. Example problems are addressed to show the powerfulness and efficacy of the methods

Analytic and Numerical Solutions of Time-Fractional Linear Schrödinger Equation

Fractional Schrödinger equation is a basic equation in fractional quantum mechanics. In this paper, we consider both analytic and numerical solutions of time-fractional linear Schrödinger Equations. This is done via a proposed semi-analytical method upon the modification of the classical Differential Transformation Method (DTM). Some illustrative examples are used; the results obtained converge faster to their exact forms. This shows that this modified version is very efficient, and reliable; as less computational work is involved, even without given up accuracy. Therefore, it is strongly recommended for both linear and nonlinear time-fractional partial differential equations (PDEs) with applications in other areas of applied sciences, management, and finance

On the Application of the Open Jackson Queuing Network

In real life, waiting for service is a common phenomenon. As a system gets congested, service delay is inevitable; as the service delay increases, waiting time in the queue gets longer. In a typical hospital, the network is made up of various departments (nodes). In this study we considered the inflow and outflow of an hospital network; this is depicted in the schematic diagram. For an efficient hospital planning, a good patient flow means that patient queuing time is minimized, while poor patient flow means the patient suffer considerable queuing delays. This paper presents the results of a study carried out in a University Hospital Centre; the queuing model adopted used the Open Jackson Queuing Network to minimize the waiting times in the queues. The data collection was done for a period of two weeks, with a week interval in order to observe the system for any anomaly. For each node, the number of arrivals and departures together with the service times were recorded at an interval of five minutes. The study showed that for a good hospital planning, the more the personnel (servers) are made to focus on their assignments, the lesser the time the patients will spend on the queue and this leads to more efficient patient flo

On Numerical Solutions of Systems of Ordinary Differential Equations by Numerical-Analytical Method

This paper considers the solutions of systems of ordinary differential equations via a numeric-analytical method referred to differential Transforms Method (DTM). For numerical interpretation, two illustrative examples are used. The results obtained show a strong agreement with their corresponding exact solutions. The method is therefore proven to be effective and reliable, and as such, can be applied to systems of ODEs involving higher orders

Numerical Solutions of Nonlinear Biochemical Model Using a Hybrid Numerical- Analytical Technique

In this paper, a hybrid numerical-analytical technique resulting from the combination of the differential transformation method and the Pade approximation technique; hereby referred to as differential transformation-Pade approximation technique (DTPAT) is introduced and applied for numerical solutions to the nonlinear biochemical reaction model. The obtained numerical results via the DTPAT are in excellent agreement with those obtained using ADM, PIM, RK4, HPM, and MPHM. The DTPAT increases the convergent rate of the series solutions obtained via the DTM, is showed to be very effective; it requires less computational work, and hence a promising technique for both linear and nonlinear systems in other areas of medical and biomedical sciences

A Numerical-Computational Technique for Solving Transformed Cauchy-Euler Equidimensional Equations of Homogeneous Type

Abstract This work considers the solution of Transformed-Cauchy-Euler differential equations via Differential Transform method (DTM). For illustration and application of the method's efficiency and reliability, two examples of order 2 and 3 are solved. The results agreed with the exact solution obtained via Laplace transform method

Coupled FCT-HP for Analytical Solutions of the Generalized Timefractional Newell-Whitehead-Segel Equation

This paper considers the generalized form of the time-fractional Newell-Whitehead-Segel model (TFNWSM) with regard to exact solutions via the application of Fractional Complex Transform (FCT) coupled with He’s polynomials method of solution. This is applied to two forms of the TFNWSM viz: nonlinear and linear forms of the time-fractional NWSM equation whose derivatives are based on Jumarie’s sense. The results guarantee the reliability and efficiency of the proposed method with less computation time while still maintaining high level of accuracy

SIR modeling of a disease spread with a detectable and undetectable infectious syndrome

This paper proposes a model for the analysis of an infectious disease spread using a renewed deterministic model of Susceptible-Infected-Recovered (SIR). The SIR is based on compartments or partitions. In this case, the contaminated (infected) class is divided into two sub-compartments: detectable and undetectable. Numerical simulations are carried out to test the obtained theoretical results, and presentations follow graphicall