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

Forecasting Analysis with the Dynamic Systems Approach on Economic Data

Abstract: This research conducts a systematic literature review to analyze forecasting with the dynamic systems approach applied to economic data. The literature was sourced from reputable indexes including Scopus, DOAJ, and Google Scholar, with a focus on publications spanning from 2013 to 2023. The synthesis of the research findings reveals that the dynamic systems approach exhibits significant flexibility in analyzing and forecasting economic data. Across diverse contexts such as business, education, and psychotherapy, this approach demonstrates its superiority in addressing the complexity and dynamics inherent in economic systems. This academic abstract emphasizes the adaptability and effectiveness of the dynamic systems approach in navigating the intricacies of economic data analysis and forecasting. The comprehensive review of literature from reputable sources contributes to a nuanced understanding of the approach's strengths and its applications in various fields. The findings underscore its significance in dealing with the challenges posed by the complex and dynamic nature of economic systems

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