## Numerical Technique

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### S F Ahmmed - One of the best experts on this subject based on the ideXlab platform.

• ##### explicit finite difference analysis of an unsteady mhd flow of a chemically reacting casson fluid past a stretching sheet with brownian motion and thermophoresis effects
Journal of King Saud University - Science, 2020
Co-Authors: Sk Rezaerabbi, S M Arifuzzaman, Tanmoy Sarkar, Md Shakhaoath Khan, S F Ahmmed
Abstract:

Abstract This study intends to elaborate the heat and mass transfer analysis of Casson nanofluid flow past a stretching sheet together with magnetohydrodynamics (MHD), thermal radiation and chemical reaction effects. The boundary layer approximations established the governing equations, i.e., time-subservient momentum, energy and diffusion balance equations. An explicit finite difference scheme was implemented as a Numerical Technique where Compaq Visual Fortran 6.6.a programming code is also developed for simulating the fluid flow system. In order to accurateness of the Numerical Technique, a stability and convergence analysis was carried out where the system was found converged at Prandtl number, Pr ≥ 0.062 and Lewis number, Le ≥ 0.025 when τ = 0.0005, ΔX = 0.8 and ΔY = 0.2. The non-dimensional outcomes are apprehended here which rely on various physical parameters. The impression of these various physical parameters on momentum and thermal boundary layers along with concentration profiles are discussed and displayed graphically. In addition, the impact of system parameters on Cf, Nu and Sh profiles with streamlines and isothermal lines are also discussed.

### Jitendra Kumar - One of the best experts on this subject based on the ideXlab platform.

• ##### an efficient semi Numerical Technique for solving nonlinear singular boundary value problems arising in various physical models
International Journal of Computer Mathematics, 2016
Co-Authors: Randhir Singh, Abdulmajid Wazwaz, Jitendra Kumar
Abstract:

An efficient semi-Numerical method is proposed for solving nonlinear singular boundary value problems BVPs arising in various physical models. We proposed a modification of the Adomian decomposition method ADM. The Technique depends on transforming the BVPs to Fredholm integral equations before establishing the recursive scheme for the solution components of a specific solution. The major advantage of the proposed method over the classical ADM or modified ADM is that it provides not only better Numerical results but also avoids unnecessary computation for determining the unknown parameters. Moreover, the proposed Technique overcomes the singularity issue at the origin . Furthermore, the convergence analysis of the proposed method is established. Two singular examples are examined to demonstrate the accuracy, applicability, and generality of the proposed method.

• ##### an efficient Numerical Technique for the solution of nonlinear singular boundary value problems
Computer Physics Communications, 2014
Co-Authors: Randhir Singh, Jitendra Kumar
Abstract:

Abstract In this work, a new Technique based on Green’s function and the Adomian decomposition method (ADM) for solving nonlinear singular boundary value problems (SBVPs) is proposed. The Technique relies on constructing Green’s function before establishing the recursive scheme for the solution components. In contrast to the existing recursive schemes based on the ADM, the proposed Technique avoids solving a sequence of transcendental equations for the undetermined coefficients. It approximates the solution in the form of a series with easily computable components. Additionally, the convergence analysis and the error estimate of the proposed method are supplemented. The reliability and efficiency of the proposed method are demonstrated by several Numerical examples. The Numerical results reveal that the proposed method is very efficient and accurate.

• ##### An efficient Numerical Technique for solving population balance equation involving aggregation, breakage, growth and nucleation
Powder Technology, 2008
Co-Authors: Jitendra Kumar, Mirko Peglow, Gerald Warnecke, Stefan Heinrich
Abstract:

Abstract A new discretization for simultaneous aggregation, breakage, growth and nucleation is presented. The new discretization is an extension of the cell average Technique developed by the authors [J. Kumar, M. Peglow, G. Warnecke, S. Heinrich, and L. Morl. Improved accuracy and convergence of discretized population balance for aggregation: The cell average Technique. Chemical Engineering Science 61 (2006) 3327–3342.]. It is shown that the cell average scheme enjoys the major advantage of simplicity for solving combined problems over other existing schemes. This is done by a special coupling of the different processes that treats all processes in a similar fashion as it handles the individual process. It is demonstrated that the new coupling makes the Technique more useful by being not only more accurate but also computationally less expensive. At first, the coupling is performed for combined aggregation and breakage problems. Furthermore, a new idea that considers the growth process as aggregation of existing particle with new small nuclei is presented. In that way the resulting discretization of the growth process becomes very simple and consistent with first two moments. Additionally, it becomes easy to combine the growth discretization with other processes. The new discretization of pure growth is a little diffusive but it predicts the first two moments exactly without any computational difficulties like appearance of negative values or instability etc. The Numerical scheme proposed in this work is consistent only with the first two moments but it can easily be extended to the consistency with any two or more than two moments. Finally, the discretization of pure and coupled problems is tasted on several analytically solvable problems.

### Mehdi Dehghan - One of the best experts on this subject based on the ideXlab platform.

• ##### A finite-difference procedure to solve weakly singular integro partial differential equation with space-time fractional derivatives
Engineering with Computers, 2020
Abstract:

The main aim of the current paper is to propose an efficient Numerical Technique for solving space-time fractional partial weakly singular integro-differential equation. The temporal variable is based on the Riemann–Liouville fractional derivative and the spatial direction is based on the Riesz fractional derivative. Thus, to achieve a Numerical Technique, the time variable is discretized using a finite difference scheme with convergence order $${{\mathcal {O}}}(\tau ^{\frac{3}{2}})$$ O ( τ 3 2 ) . Also, the space variable is discretized using a finite difference scheme with second-order accuracy. Furthermore, for the time-discrete and the full-discrete schemes error estimate has been presented to show the unconditional stability and convergence of the developed Numerical method. Finally, two test problems have been illustrated to verify the efficiency, applicability and simplicity of the proposed Technique.

• ##### an efficient Technique based on finite difference finite element method for solution of two dimensional space multi time fractional bloch torrey equations
Applied Numerical Mathematics, 2018
Abstract:

Abstract The main aim of the current paper is to propose an efficient Numerical Technique for solving two-dimensional space-multi-time fractional Bloch–Torrey equations. The current research work is a generalization of [6] . The temporal direction is based on the Caputo fractional derivative with multi-order fractional derivative and the spatial directions are based on the Riemann–Liouville fractional derivative. Thus, to achieve a Numerical Technique, the time variable is discretized using a finite difference scheme with convergence order O ( τ 2 − α ) . Also, the space variable is discretized using the finite element method. Furthermore, for the time-discrete and the full-discrete schemes error estimate has been presented to show the unconditional stability and convergence of the developed Numerical method. Finally, four test problems have been illustrated to verify the efficiency and simplicity of the proposed Technique on irregular computational domains.

• ##### a meshless based Numerical Technique for traveling solitary wave solution of boussinesq equation
Applied Mathematical Modelling, 2012
Co-Authors: Mehdi Dehghan, Rezvan Salehi
Abstract:

Abstract In this paper, we employ the boundary-only meshfree method to find out Numerical solution of the classical Boussinesq equation in one dimension. The proposed method in the current paper is a combination of boundary knot method and meshless analog equation method. The boundary knot Technique is an integration free, boundary-only, meshless method which is used to avoid the known disadvantages of the method of fundamental solution. Also, we use the meshless analog equation method to replace the nonlinear governing equation with an equivalent nonhomogeneous linear equation. A predictor–corrector scheme is proposed to solve the resulted differential equation of the collocation. The Numerical results and conclusions are obtained for both the ‘good’ and the ‘bad’ Boussinesq equations.

• ##### a Numerical Technique for solving fractional optimal control problems
Computers & Mathematics With Applications, 2011
Co-Authors: Ali Lotfi, Mehdi Dehghan, S A Yousefi
Abstract:

This paper presents a Numerical method for solving a class of fractional optimal control problems (FOCPs). The fractional derivative in these problems is in the Caputo sense. The method is based upon the Legendre orthonormal polynomial basis. The operational matrices of fractional Riemann-Liouville integration and multiplication, along with the Lagrange multiplier method for the constrained extremum are considered. By this method, the given optimization problem reduces to the problem of solving a system of algebraic equations. By solving this system, we achieve the solution of the FOCP. Illustrative examples are included to demonstrate the validity and applicability of the new Technique.

• ##### The solution of a second-order nonlinear differential equation with Neumann boundary conditions using semi-orthogonal B-spline wavelets
International Journal of Computer Mathematics, 2006
Abstract:

A Numerical Technique for solving a second-order nonlinear Neumann problem is presented. The authors’ approach is based on semi-orthogonal B-spline wavelets. Two test problems are presented and Numerical results are tabulated to show the efficiency of the proposed Technique for the studied problem.

### J E Roy - One of the best experts on this subject based on the ideXlab platform.

• ##### a Numerical Technique for computing the values of plane wave scattering coefficients of a general scatterer
IEEE Transactions on Antennas and Propagation, 2009
Co-Authors: J E Roy
Abstract:

The results of a Numerical Technique for computing the plane wave scattering coefficients of a general scatterer are presented. The Technique is tailored herein to the case where the scatterer is a general slab and the Technique is implemented with the FDTD method of the scattered field formulation. Since the Technique relies on the use of a Maxwellian beam of dominant polarization as the excitation within the FDTD simulation, this paper presents also an improved scheme for synthesizing such a beam. Window averaging is also presented as a new scheme for mitigating the effects of aperture truncation. Validation of the Technique revealed that the use of a non-Maxwellian Gaussian beam of uniform polarization produced erroneous values of the plane wave scattering coefficients. When used with a Maxwellian beam excitation, however, the Technique showed to be trustworthy, stable and accurate, even for lossy media. Convergence test results revealed that the accuracy of the values of plane wave scattering coefficients decreased much faster as the conductivity of the medium increased than what would be expected from Numerical anisotropy. Finally, poor accuracy results are reported when the scattered field illuminates strongly the edges or corners of the integration box around a finite-size slab.

### Sk Rezaerabbi - One of the best experts on this subject based on the ideXlab platform.

• ##### explicit finite difference analysis of an unsteady mhd flow of a chemically reacting casson fluid past a stretching sheet with brownian motion and thermophoresis effects
Journal of King Saud University - Science, 2020
Co-Authors: Sk Rezaerabbi, S M Arifuzzaman, Tanmoy Sarkar, Md Shakhaoath Khan, S F Ahmmed
Abstract:

Abstract This study intends to elaborate the heat and mass transfer analysis of Casson nanofluid flow past a stretching sheet together with magnetohydrodynamics (MHD), thermal radiation and chemical reaction effects. The boundary layer approximations established the governing equations, i.e., time-subservient momentum, energy and diffusion balance equations. An explicit finite difference scheme was implemented as a Numerical Technique where Compaq Visual Fortran 6.6.a programming code is also developed for simulating the fluid flow system. In order to accurateness of the Numerical Technique, a stability and convergence analysis was carried out where the system was found converged at Prandtl number, Pr ≥ 0.062 and Lewis number, Le ≥ 0.025 when τ = 0.0005, ΔX = 0.8 and ΔY = 0.2. The non-dimensional outcomes are apprehended here which rely on various physical parameters. The impression of these various physical parameters on momentum and thermal boundary layers along with concentration profiles are discussed and displayed graphically. In addition, the impact of system parameters on Cf, Nu and Sh profiles with streamlines and isothermal lines are also discussed.