The Experts below are selected from a list of 126 Experts worldwide ranked by ideXlab platform

Teh Yuan Ying - One of the best experts on this subject based on the ideXlab platform.

  • Numerical solution of first order initial value Problem using 4-stage sixth order Gauss-Kronrod-Radau IIA method
    2020
    Co-Authors: Teh Yuan Ying, Nazeeruddin Yaacob
    Abstract:

    In this paper, a new implicit Runge-Kutta method which based on a 4-point Gauss-Kronrod-Radau II quadrature formula is developed.The resulting implicit method is a 4-stage sixth order Gauss-Kronrod-Radau IIA method, or in brief as GKRM(4,6)-IIA. GKRM(4,6)-IIA requires four function of evaluations at each integration step and it gives accuracy of order six.In addition, GKRM(4,6)-IIA has stage order four and being L-stable. Numerical experiments compare the accuracy between GKRM(4,6)-IIA and the classical 3-stage sixth order Gauss-Legendre method in solving some test Problems. Numerical results reveal that GKRM(4,6)-IIA is more accurate than the 3-stage sixth order Gauss-Legendre method because GKRM(4,6)-IIA has higher stage orde

  • Numerical solution of first order initial value Problem using quartic spline method
    2015
    Co-Authors: Teh Yuan Ying, Azizan Saaban
    Abstract:

    Any first order initial value Problem can be integrated numerically by discretizing the interval of integration into a number of subintervals, either with equally distributed grid points or non-equally distributed grid points. Hence, as the integration advances, the numerical solutions at the grid points are calculated and being known. However, the numerical solutions between the grid points remain unknown. This will form difficulty to individuals who wish to study a particular solution which may not fall on the grid points. Therefore, some sorts of interpolation techniques are needed to deal with such difficulty. Spline interpolation technique remains as a well known approach to approximate the numerical solution of a first order initial value Problem, not only at the grid points but also everywhere between the grid points. In this short article, a new quartic spline method has been derived to obtain the numerical solution for first order initial value Problem. The key idea of the derivation is to treat ...

  • Numerical solution of second order boundary value Problem using rational method
    2015
    Co-Authors: Teh Yuan Ying
    Abstract:

    Numerical methods that are based on rational functions or better known as rational methods were discovered 60 years ago when they were initially used to deal with Problem whose solution possess singularity. Ever since then, a number of studies have discovered various types of rational methods and used them to solve more general first order initial value Problems such as stiff Problem and Problem with oscillatory property. Previous studies showed the reliability of rational methods in solving first order initial value Problem through numerical experimentations. In this article, we have investigated the solvability of several existing fourth order rational methods to second order boundary value Problem by replacing it with a coupled of first order initial value Problems. Such replacement yielded the shooting method. As part of the investigation, these rational methods were compared among themselves and also compared with the 4-stage fourth order explicit Runge-Kutta method. Numerical experimentations seemed...

  • An explicit two-step rational method for the numerical solution of first order initial value Problem
    2014
    Co-Authors: Teh Yuan Ying
    Abstract:

    An explicit two-step, second order rational method for the numerical solution of first order initial value Problems is introduced in this paper. Existing rational multistep methods required the computations of higher derivatives from a given initial value Problem. However, the new two-step rational method does not require any computation of these higher derivatives, and thus save up some computational cost. Numerical results showed that the new rational multistep method and existing rational multistep method are found to have comparable accuracy in solving first order initial value Problems.

  • Numerical solution of first order initial value Problem using 7-stage tenth order Gauss-Kronrod-Lobatto IIIA method
    2013
    Co-Authors: Teh Yuan Ying, Nazeeruddin Yaacob
    Abstract:

    In this paper, a new implicit Runge-Kutta method which based on a 4-point Gauss-Kronrod-Radau II quadrature formula is developed. The resulting implicit method is a 4-stage sixth order Gauss-Kronrod-Radau IIA method, or in brief as GKRM(4,6)-IIA. GKRM(4,6)-IIA requires four function of evaluations at each integration step and it gives accuracy of order six. In addition, GKRM(4,6)-IIA has stage order four and being L-stable. Numerical experiments compare the accuracy between GKRM(4,6)-IIA and the classical 3-stage sixth order Gauss-Legendre method in solving some test Problems. Numerical results reveal that GKRM(4,6)-IIA is more accurate than the 3-stage sixth order Gauss-Legendre method because GKRM(4,6)-IIA has higher stage order.

D. S. Palimkar - One of the best experts on this subject based on the ideXlab platform.

Syed Tauseef Mohyuddin - One of the best experts on this subject based on the ideXlab platform.

  • unsteady radiative flow of chemically reacting fluid over a convectively heated stretchable surface with cross diffusion gradients
    International Journal of Thermal Sciences, 2017
    Co-Authors: Naveed Ahmed, Umar Khan, Syed Tauseef Mohyuddin
    Abstract:

    Abstract The unsteady radiative flow of chemically reacting fluid over bilaterally stretching surface is under consideration. The surface is convectively heated and influence of thermal and concentration gradients is also taken into account. The resulting nondimensional form of the radiative flow model is obtained after utilizing the feasible set of self-similar variables. Further, model is treated numerically with the help of Runge-Kutta scheme after reduced the model into coupled system of first order initial value Problem. Influence of the different flow parameters specially Biot's number, Radiation and chemical reaction parameters are discussed for different values. Also, steady and two dimensional case of the current model is plotted. The graphically comparison between thermal and concentration fields is also provided in the presence and absence of thermal and concentration gradients. Impact of ingrained physical parameters on skin friction coefficient, heat and mass transfer gradients performed numerically. The significant effects of Radiation and chemical reaction parameters on thermal and concentration of the fluid observed. Finally, core findings of the study are mentioned in the last section of the letter.

  • influence of thermal radiation and viscous dissipation on squeezed flow of water between riga plates saturated with carbon nanotubes
    Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2017
    Co-Authors: Naveed Ahmed, Umar Khan, Syed Tauseef Mohyuddin
    Abstract:

    Abstract This article aims to explore the flow of water containing the Carbon nanotubes in the appropriate geometry of Riga plates. Thermal radiation and viscous dissipation effects are also taken into account. Resulting nonlinear flow model of nanofluid is obtained after entreating the feasible dimensionless variables in to the system of nonlinear partial differential equations. Solutions of the model is then performed both numerically and analytically. For numerical treatment of the model, Runge-Kutta numerical scheme is utilized after reducing the nonlinear system in to the system of first order initial value Problem and for analytical solution, Adomians decomposition method is followed. The error analysis is also tabulated which shows the validity of employed analytical technique. The influence of different dimensionless flow parameters on velocity field, temperature field, skin friction and local rate of heat transfer is also part of the discussion. It is observed that for varying Eckert and local Eckert numbers, temperature filed is an increasing function. On the other hand for radiation parameter, temperature starts decreasing. Skin friction starts decreasing for higher values of squeeze number and for radiation parameter, local rate of heat transfer decreases. Finally, some concluding observations are highlighted in the last section.

Khalida Inayat Noor - One of the best experts on this subject based on the ideXlab platform.

  • Variational Iteration Method for Solving Flierl-petviashivili Equation Using He's Polynomials and PadeApproximants
    2020
    Co-Authors: Syed Tauseef Mohyud-din, Muhammad Aslam Noor, Khalida Inayat Noor
    Abstract:

    In this paper, we apply Variational Iteration Method using He's Polynomials (VIMHP) for finding a solution of Flierl-Petviashivili (FP) equation. The approach introduces a new transformation which is required for the conversion of the Flierl-Petviashivili equation to a first order initial value Problem and a reliable framework designed to overcome the difficulty of the singular point at x = 0. The proposed method is applied to the reformulated First-Order initial value Problem which gives the solution in terms of transformed variable. The desired series of solution is obtained by making use of the inverse transformation. The fact that the VIMHP solves nonlinear Problems without using Adomian's polynomials is a clear advantage of this algorithm over the decomposition method.

  • COMPARISON AND COUPLING OF POLYNOMIALS FOR FLIERL- PETVIASHIVILI EQUATION
    Mathematical & Computational Applications, 2010
    Co-Authors: Syed Tauseef Mohyud-din, Muhammad Aslam Noor, Khalida Inayat Noor
    Abstract:

    This paper outlines a comparison of the couplings of He’s and Adomian’s polynomials with correction functional of variational iteration method (VIM) to investigate a solution of Flierl-Petviashivili (FP) equation which plays a very important role in mathematical physics, engineering and applied sciences. These elegant couplings give rise to two modified versions of VIM which are very efficient in solving initial and boundary value Problems of diversified nature. Moreover, we also introduces a new transformation which is required for the conversion of the Flierl-Petviashivili equation to a first order initial value Problem and a reliable framework designed to overcome the difficulty of the singular point at x = 0. The proposed modified versions are applied to the reformulated first order initial value Problem which gives the solution in terms of transformed variable. The desired series of solution is obtained by making use of the inverse transformation. It is observed that the modification based on He’s polynomials is much easier to implement and is more user friendly.

Nazeeruddin Yaacob - One of the best experts on this subject based on the ideXlab platform.

  • Numerical solution of first order initial value Problem using 4-stage sixth order Gauss-Kronrod-Radau IIA method
    2020
    Co-Authors: Teh Yuan Ying, Nazeeruddin Yaacob
    Abstract:

    In this paper, a new implicit Runge-Kutta method which based on a 4-point Gauss-Kronrod-Radau II quadrature formula is developed.The resulting implicit method is a 4-stage sixth order Gauss-Kronrod-Radau IIA method, or in brief as GKRM(4,6)-IIA. GKRM(4,6)-IIA requires four function of evaluations at each integration step and it gives accuracy of order six.In addition, GKRM(4,6)-IIA has stage order four and being L-stable. Numerical experiments compare the accuracy between GKRM(4,6)-IIA and the classical 3-stage sixth order Gauss-Legendre method in solving some test Problems. Numerical results reveal that GKRM(4,6)-IIA is more accurate than the 3-stage sixth order Gauss-Legendre method because GKRM(4,6)-IIA has higher stage orde

  • Numerical solution of first order initial value Problem using 7-stage tenth order Gauss-Kronrod-Lobatto IIIA method
    2013
    Co-Authors: Teh Yuan Ying, Nazeeruddin Yaacob
    Abstract:

    In this paper, a new implicit Runge-Kutta method which based on a 4-point Gauss-Kronrod-Radau II quadrature formula is developed. The resulting implicit method is a 4-stage sixth order Gauss-Kronrod-Radau IIA method, or in brief as GKRM(4,6)-IIA. GKRM(4,6)-IIA requires four function of evaluations at each integration step and it gives accuracy of order six. In addition, GKRM(4,6)-IIA has stage order four and being L-stable. Numerical experiments compare the accuracy between GKRM(4,6)-IIA and the classical 3-stage sixth order Gauss-Legendre method in solving some test Problems. Numerical results reveal that GKRM(4,6)-IIA is more accurate than the 3-stage sixth order Gauss-Legendre method because GKRM(4,6)-IIA has higher stage order.

  • Numerical Solution of First Order Initial Value Problem Using 5-Stage Eighth Order Gauss-Kronrod Method
    2011
    Co-Authors: Teh Yuan Ying, Nazeeruddin Yaacob
    Abstract:

    In this paper, two new implicit Runge-Kutta methods which based on a 5-point Gauss-Kronrod quadrature formula are developed. The resulting implicit methods are two 5-stage eighth order Gauss-Kronrod methods, or in brief as GKM1(5,8) and GKM2(5,8) respectively. Theoretical analyses show that GKM1(5,8) has stage order 5 while GKM2(5,8) has stage order 3, but both methods are A-stable. Numerical experimentations have compared the accuracy among GKM1(5,8), GKM2(5,8) and the classical 4-stage eighth order Gauss-Legendre method. Numerical results have showed that GKM1(5,8) is the most accurate compare to GKM2(5,8) and the classical 4-stage eighth order Gauss-Legendre method because GKM1(5,8) has the highest stage order.