A Semi-Analytical Method for The Solution of Linear And Nonlinear Newell-Whitehead-Segel Equations

The aim of this work is to use a semi-analytical method “Reduced Differential Transform Method (RDTM)” for the solution of linear and nonlinear Newell-Whitehead-Segel Equations (NWSE). RDTM does not require linearization, transformation, discretization, perturbation or restrictive assumptions. To determine the performance measure of the RDTM, two illustrative examples were considered. The comparative study of the results obtained via the RDTM was compared with that of the exact solution. Hence, RDTM offers solutions with easily computable components as convergent series and is an alternative approach that overcomes the shortcoming of complex calculations of differential transform method

Determination of the Order and the Error Constant of an Implicit Linear-Four Step Method

The aim of this work is to determine the order and the error constant of an implicit linear-four step method namely “The Quade’s method”. From the results generated, It is observed that the method is of order six and the error constant is obtained as . The Local Truncation Error (LTE) of the general implicit linear four-step is obtained

On a New Technique for the Solution of the Black-Scholes Partial Differential Equation for European Call Option

This paper presents a new technique for the solution of the Black-Scholes partial differential equation for European call option using a method based on the modified Mellin transform. We also used the modified Mellin transform method to determine the price of European call option. The modified Mellin transform method is mutually consistent and agrees with the values of Black-Scholes model as shown i

On the Comparative Study of Some Numerical Methods for Vanilla Option Valuation

This paper presents some numerical methods for vanilla option valuation namely binomial tree model, Crank Nicolson method and Monte Carlo method. Binomial model is widely used in the finance community for numerical valuation of a wide variety of option models, due primarily to its ease of implementation and pedagogical appeal. Crank Nicolson approach seeks the discretization of the differential operators in the continuous Black Scholes model. Monte Carlo method simulates the random movement of the asset prices and provides a probabilistic solution to the option pricing models. We discuss the strengths, drawbacks and the performance of the methods under consideration. However, binomial model is the most accurate and converges faster than its two counterparts; Crank Nicolson method and Monte Carlo method

Black-Scholes Partial Differential Equation In The Mellin Transform Domain

Abstract: This paper presents Black-Scholes partial differential equation in the Mellin transform domain. The Mellin transform method is one of the most popular methods for solving diffusion equations in many areas of science and technology. This method is a powerful tool used in the valuation of options. We extend the Mellin transform method proposed by Panini and Srivasta

Modelling of creep behaviour of a rotating disc in the presence of load and variable thickness by using seth transition theory

The purpose of this paper is to present study of creep behaviour of a rotating disc in the presence of load and thickness by using Seth's transition theory. It has been observed that a flat rotating disc made of compressible as well as incompressible material with load E-1 = 10, increases the possibility of fracture at the bore. It Is also shown that a rotating disc of incompressible material and thickness that increases radially experiences higher creep rates at the internal surface in comparison to a disc of compressible material. The model proposed in this paper is used in mechanical and electronic devices. They have extensive practical engineering applications such as in steam and gas turbines, turbo generators, flywheel of internal combustion engines, turbojet engines, reciprocating engines, centrifugal compressors and brake discs

Modelling of creep behaviour of a rotating disc in the presence of load and variable thickness by using seth transition theory

The purpose of this paper is to present study of creep behaviour of a rotating disc in the presence of load and thickness by using Seth's transition theory. It has been observed that a flat rotating disc made of compressible as well as incompressible material with load E-1 = 10, increases the possibility of fracture at the bore. It Is also shown that a rotating disc of incompressible material and thickness that increases radially experiences higher creep rates at the internal surface in comparison to a disc of compressible material. The model proposed in this paper is used in mechanical and electronic devices. They have extensive practical engineering applications such as in steam and gas turbines, turbo generators, flywheel of internal combustion engines, turbojet engines, reciprocating engines, centrifugal compressors and brake discs

ON MATHEMATICAL MODEL FOR THE STUDY OF TRAFFIC FLOW ON THE HIGH WAYS

This paper presents mathematical model for the study of traffic flow on the highways. The effect of the density of cars on the overall interactions of the vehicles along a given distance of the road was investigated. We also observed that the density of cars per mile affects the net rate of interaction between them

Convergent Numerical Method Using Transcendental Function of Exponential Type to Solve Continuous Dynamical Systems

This paper presents a numerical integration method recentlyproposed by means of an interpolating function involving a transcendentalfunction of exponential type for the solution of continuous dynamicalsystems, that is, the initial value problems (IVPs) in ordinary differentialequations (ODEs). The analysis of the local truncation error³Tn (h)´, orderof convergence, consistency and the stability of the proposed methodhave been investigated in the present study. The principal term of Tn (h)for the method has been derived via Taylor’s series expansion. The standardtest problem is taken into account to investigate the linear stabilityregion and the corresponding stability interval of the method. It is observedthat the newly proposed numerical integration method is secondorder convergent, consistent and conditionally stable. In order to test theperformance measure of the proposed method, five IVPs of varying naturehave been illustrated in the context of the maximum absolute global relativeerrors, the absolute relative errors computed at the final mesh point ofthe integration interval under consideration and the `2¡ error norm. Furthermore,the results are compared with two existing second order explicitnumerical methods taken from the relevant literature. The so far obtainedresults have demonstrated that the proposed numerical integration methodagrees with the second order convergence based upon the analysis conducted.Hence the proposed method is considered to be a good approachfor finding the solution of different types of IVPs in ODEs