Abanum Godspower | University of Port Harcourt (original) (raw)

Uploads

Papers by Abanum Godspower

This paper has considered the numerical solution of the Heston stochastic volatility model (HSVM)... more This paper has considered the numerical solution of the Heston stochastic volatility model (HSVM) using the Elzaki transform method (ETM). The proposed method seeks the approximate solution of the HSVM by implementing its properties on the HSVM. The ETM proposes the solution as a rapid convergent series that represents the precise interpretation of the HSVM in real life situations. Also, the reckless interest rate is choice as -2.01 in correspondence with [4]. Numerical evidences were obtained with the help of Maple 18 software, and are compared with the homotopy perturbation method (HPM) and variational iteration method (VIM) found in the literature [4]

Mathematical theory and modeling, 2018

In this paper, we consider the numerical treatment of the nonlinear parabolic-hyperbolic partial ... more In this paper, we consider the numerical treatment of the nonlinear parabolic-hyperbolic partial differential equation of the form...... More details are available in the PDF of article.

International Journal of Mathematics Trends and Technology, 2020

The dependent variable called Normal Agriculture changes as the independent variable time changes... more The dependent variable called Normal Agriculture changes as the independent variable time changes that is the yields of a normal agriculture variable changes deterministically as the length of the growing season changes when all the model parameter values are fixed. However, when the model parameter values 1 2 are decrease, the normal agricultural variable also changes. By comparing the patterns of growth in these two interacting normal agricultural data, we have finite instance of biodiversity due to the application of four numerical methods such as ODE45, ODE23, ODE23tb and ODE15s. We have found the numerical prediction upon using these four numerical methods which are similar and robust, hence we have considered ODE45 numerical simulation to be computationally more efficient than the other three methods. The novel result we have obtained in this study have not been seen elsewhere. These are presented and discussed quantitatively.

International Journal of Mathematic Trend and Technology, 2020

The dependent variable called Normal Agriculture changes as the independent variable time changes... more The dependent variable called Normal Agriculture changes as the independent variable time changes that is the yields of a normal agriculture variable changes deterministically as the length of the growing season changes when all the model parameter values are fixed. However, when the model parameter values 1 2 are decrease, the normal agricultural variable also changes. By comparing the patterns of growth in these two interacting normal agricultural data, we have finite instance of biodiversity due to the application of four numerical methods such as ODE45, ODE23, ODE23tb and ODE15s. We have found the numerical prediction upon using these four numerical methods which are similar and robust, hence we have considered ODE45 numerical simulation to be computationally more efficient than the other three methods. The novel result we have obtained in this study have not been seen elsewhere. These are presented and discussed quantitatively.

In this paper, the Modified variational iteration method using canonical polynomials(MVIMCP) whic... more In this paper, the Modified variational iteration method using canonical polynomials(MVIMCP) which is an elegant combination of the variational iteration method and the canonical polynomials method employed for resolving boundary value problems of seventh order. The approximate solution of the problem is obtained in terms of rapidly convergent series. The scheme is tested for some examples and the obtained result demonstrates the reliability and efficiency of the proposed method.

IOSR Journal of Mathematics

This paper has considered the numerical solution of the Heston stochastic volatility model (HSVM)... more This paper has considered the numerical solution of the Heston stochastic volatility model (HSVM) using the Elzaki transform method (ETM). The proposed method seeks the approximate solution of the HSVM by implementing its properties on the HSVM. The ETM proposes the solution as a rapid convergent series that represents the precise interpretation of the HSVM in real life situations. Also, the reckless interest rate is choice as -2.01 in correspondence with [4]. Numerical evidences were obtained with the help of Maple 18 software, and are compared with the homotopy perturbation method (HPM) and variational iteration method (VIM) found in the literature [4]

International Journal of Advances in Scientific Research and Engineering , 2018

In this research work, we focused on the application of the first kind Chebychev polynomials as b... more In this research work, we focused on the application of the first kind Chebychev polynomials as basis functions for the numerical solution of first and second order ordinary differential equations. For this purpose, the variational iteration method (VIM) was adopted as an iterative scheme to generate the required approximate solutions. The VIM with the Chebychev polynomials was applied to some selected linear and nonlinear problems for experimentations, and the resulting numerical evidence shows that it is effective and accurate.

In this paper, we consider the numerical treatment of the nonlinear parabolic-hyperbolic partial ... more In this paper, we consider the numerical treatment of the nonlinear parabolic-hyperbolic partial differential equation of the form (P-H PDE) u t − ∆u tt − ∆ − Fu = 0, where Fu is the nonlinear term, and ∆∈ ℝ 1 is a Laplace operator. Here, the variational iteration method (VIM) was employed to examine the convergence of solution of the nonlinear P-H PDE. Results obtained showed that there is a rapid rate of convergence of the approximate solution to the exact solution as the number of iterations increases. All computational framework of the research were performed using Maple 18 software. Keywords: Variational iteration method, Nonlinear PDE, Lagrange Multiplier, Linear differential operator 1. Introduction Most physical problems that are expressed using more than one variable involve partial derivatives. They are even more significant in modeling real life situations such as shock waves (Burgers equation), gas dynamics (gas dynamic equation), steady state distribution of heat in a two-dimensional plain (Poisson equation), steady state problems involving incompressible fluid in a two-dimensional plain (Poisson equation), the effect of gravitational force on the potential energy of a point in a two-dimensional region (Poisson equation) etc. The parabolic partial differential equation (P-PDE) is very significant in the study of gas diffusion, which is generally called the diffusion equation. Most conventional analytic solvers (such as the integral transform method (ITM), method of characteristic (MOC), separation of variable methods, and the change of variable methods, etc) for partial differential equation over the years proved complex and difficult to handle, and does not have a precise and concise solution that can effectively and sufficiently interpret the external and internal variables of the model in consideration. This defect has attributed to the use of numerical methods by researchers in recent years for the approximation of the analytic solutions of partial differential equations. Popular numerical schemes developed and implemented over the years for partial differential equations include; the finite difference method, the finite element method, the cranck-Nicolsone method, the Bender-Schimdt method etc. The variational iteration method (IVM) was first proposed by the Chinese mathematician, J.H. He in 1998. The method has proved effective in solving both linear and nonlinear problems in differential equations, integral equations, boundary value problems, initial value problems, integro-differential problems etc. For instance, He (2000) seeks the numerical solution of autonomous ordinary

This paper has considered the numerical solution of the Heston stochastic volatility model (HSVM)... more This paper has considered the numerical solution of the Heston stochastic volatility model (HSVM) using the Elzaki transform method (ETM). The proposed method seeks the approximate solution of the HSVM by implementing its properties on the HSVM. The ETM proposes the solution as a rapid convergent series that represents the precise interpretation of the HSVM in real life situations. Also, the reckless interest rate is choice as -2.01 in correspondence with [4]. Numerical evidences were obtained with the help of Maple 18 software, and are compared with the homotopy perturbation method (HPM) and variational iteration method (VIM) found in the literature [4]

Mathematical theory and modeling, 2018

In this paper, we consider the numerical treatment of the nonlinear parabolic-hyperbolic partial ... more In this paper, we consider the numerical treatment of the nonlinear parabolic-hyperbolic partial differential equation of the form...... More details are available in the PDF of article.

International Journal of Mathematics Trends and Technology, 2020

The dependent variable called Normal Agriculture changes as the independent variable time changes... more The dependent variable called Normal Agriculture changes as the independent variable time changes that is the yields of a normal agriculture variable changes deterministically as the length of the growing season changes when all the model parameter values are fixed. However, when the model parameter values 1 2 are decrease, the normal agricultural variable also changes. By comparing the patterns of growth in these two interacting normal agricultural data, we have finite instance of biodiversity due to the application of four numerical methods such as ODE45, ODE23, ODE23tb and ODE15s. We have found the numerical prediction upon using these four numerical methods which are similar and robust, hence we have considered ODE45 numerical simulation to be computationally more efficient than the other three methods. The novel result we have obtained in this study have not been seen elsewhere. These are presented and discussed quantitatively.

International Journal of Mathematic Trend and Technology, 2020

The dependent variable called Normal Agriculture changes as the independent variable time changes... more The dependent variable called Normal Agriculture changes as the independent variable time changes that is the yields of a normal agriculture variable changes deterministically as the length of the growing season changes when all the model parameter values are fixed. However, when the model parameter values 1 2 are decrease, the normal agricultural variable also changes. By comparing the patterns of growth in these two interacting normal agricultural data, we have finite instance of biodiversity due to the application of four numerical methods such as ODE45, ODE23, ODE23tb and ODE15s. We have found the numerical prediction upon using these four numerical methods which are similar and robust, hence we have considered ODE45 numerical simulation to be computationally more efficient than the other three methods. The novel result we have obtained in this study have not been seen elsewhere. These are presented and discussed quantitatively.

In this paper, the Modified variational iteration method using canonical polynomials(MVIMCP) whic... more In this paper, the Modified variational iteration method using canonical polynomials(MVIMCP) which is an elegant combination of the variational iteration method and the canonical polynomials method employed for resolving boundary value problems of seventh order. The approximate solution of the problem is obtained in terms of rapidly convergent series. The scheme is tested for some examples and the obtained result demonstrates the reliability and efficiency of the proposed method.

IOSR Journal of Mathematics

This paper has considered the numerical solution of the Heston stochastic volatility model (HSVM)... more This paper has considered the numerical solution of the Heston stochastic volatility model (HSVM) using the Elzaki transform method (ETM). The proposed method seeks the approximate solution of the HSVM by implementing its properties on the HSVM. The ETM proposes the solution as a rapid convergent series that represents the precise interpretation of the HSVM in real life situations. Also, the reckless interest rate is choice as -2.01 in correspondence with [4]. Numerical evidences were obtained with the help of Maple 18 software, and are compared with the homotopy perturbation method (HPM) and variational iteration method (VIM) found in the literature [4]

International Journal of Advances in Scientific Research and Engineering , 2018

In this research work, we focused on the application of the first kind Chebychev polynomials as b... more In this research work, we focused on the application of the first kind Chebychev polynomials as basis functions for the numerical solution of first and second order ordinary differential equations. For this purpose, the variational iteration method (VIM) was adopted as an iterative scheme to generate the required approximate solutions. The VIM with the Chebychev polynomials was applied to some selected linear and nonlinear problems for experimentations, and the resulting numerical evidence shows that it is effective and accurate.

In this paper, we consider the numerical treatment of the nonlinear parabolic-hyperbolic partial ... more In this paper, we consider the numerical treatment of the nonlinear parabolic-hyperbolic partial differential equation of the form (P-H PDE) u t − ∆u tt − ∆ − Fu = 0, where Fu is the nonlinear term, and ∆∈ ℝ 1 is a Laplace operator. Here, the variational iteration method (VIM) was employed to examine the convergence of solution of the nonlinear P-H PDE. Results obtained showed that there is a rapid rate of convergence of the approximate solution to the exact solution as the number of iterations increases. All computational framework of the research were performed using Maple 18 software. Keywords: Variational iteration method, Nonlinear PDE, Lagrange Multiplier, Linear differential operator 1. Introduction Most physical problems that are expressed using more than one variable involve partial derivatives. They are even more significant in modeling real life situations such as shock waves (Burgers equation), gas dynamics (gas dynamic equation), steady state distribution of heat in a two-dimensional plain (Poisson equation), steady state problems involving incompressible fluid in a two-dimensional plain (Poisson equation), the effect of gravitational force on the potential energy of a point in a two-dimensional region (Poisson equation) etc. The parabolic partial differential equation (P-PDE) is very significant in the study of gas diffusion, which is generally called the diffusion equation. Most conventional analytic solvers (such as the integral transform method (ITM), method of characteristic (MOC), separation of variable methods, and the change of variable methods, etc) for partial differential equation over the years proved complex and difficult to handle, and does not have a precise and concise solution that can effectively and sufficiently interpret the external and internal variables of the model in consideration. This defect has attributed to the use of numerical methods by researchers in recent years for the approximation of the analytic solutions of partial differential equations. Popular numerical schemes developed and implemented over the years for partial differential equations include; the finite difference method, the finite element method, the cranck-Nicolsone method, the Bender-Schimdt method etc. The variational iteration method (IVM) was first proposed by the Chinese mathematician, J.H. He in 1998. The method has proved effective in solving both linear and nonlinear problems in differential equations, integral equations, boundary value problems, initial value problems, integro-differential problems etc. For instance, He (2000) seeks the numerical solution of autonomous ordinary