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Papers by ram k pandey

Research paper thumbnail of Semi-Analytic Solutions of Electrohydrodynamic Flow in a Circular Cylinder Conduit

Research paper thumbnail of An Efficient Computational Method for the Time-Space Fractional Klein-Gordon Equation

Frontiers in Physics, 2020

Research paper thumbnail of Solution of Electrohydrodynamic Flow Equation Using an Orthogonal Collocation Method Based on Mixed Interpolation

Journal of Applied Mathematics and Physics, 2018

Research paper thumbnail of Semi-analytic algorithms for the electrohydrodynamic flow equation

Journal of Theoretical and Applied Physics, 2012

In this paper, we consider the nonlinear boundary value problem for the electrohydrodynamic (EHD)... more In this paper, we consider the nonlinear boundary value problem for the electrohydrodynamic (EHD) flow of a fluid in an ion-drag configuration in a circular cylindrical conduit. This phenomenon is governed by a nonlinear second-order differential equation. The degree of nonlinearity is determined by a nondimensional parameter α. We present two semi-analytic algorithms to solve the EHD flow equation for various values of relevant parameters based on optimal homotopy asymptotic method (OHAM) and optimal homotopy analysis method. In 1999, Paullet has shown that for large α, the solutions are qualitatively different from those calculated by Mckee in 1997. Both of our solutions obtained by OHAM and optimal homotopy analysis method are qualitatively similar with Paullet’s solutions.

Research paper thumbnail of Generalized Abel Inversion Using Extended Hat Functions Operational Matrix

International Journal of Analysis, 2013

Abel type integral equations play a vital role in the study of compressible flows around axially ... more Abel type integral equations play a vital role in the study of compressible flows around axially symmetric bodies. The relationship between emissivity and the measured intensity, as measured from the outside cylindrically symmetric, optically thin extended radiation source, is given by this equation as well. The aim of the present paper is to propose a stable algorithm for the numerical inversion of the following generalized Abel integral equation:I(y)=a(y)∫αy((rμ-1ε(r))/(yμ-rμ)γ)dr+b(y)∫yβ((rμ-1ε(r)) /(rμ-yμ)γ)dr,α≤y≤β,0<γ<1, using our newly constructed extended hat functions operational matrix of integration, and give an error analysis of the algorithm. The earlier numerical inversions available for the above equation assumed eithera(y)=0orb(y)=0.

Research paper thumbnail of Optimal Variational Asymptotic Method for Nonlinear Fractional Partial Differential Equations

International Scholarly Research Notices, 2014

We propose optimal variational asymptotic method to solve time fractional nonlinear partial diffe... more We propose optimal variational asymptotic method to solve time fractional nonlinear partial differential equations. In the proposed method, an arbitrary number of auxiliary parameters γ0,γ1,γ2,… and auxiliary functions H0(x),H1(x),H2(x),… are introduced in the correction functional of the standard variational iteration method. The optimal values of these parameters are obtained by minimizing the square residual error. To test the method, we apply it to solve two important classes of nonlinear partial differential equations: (1) the fractional advection-diffusion equation with nonlinear source term and (2) the fractional Swift-Hohenberg equation. Only few iterations are required to achieve fairly accurate solutions of both the first and second problems.

Research paper thumbnail of Analytic algorithms for Some Models of Nonlinear Age–Structured Population Dynamics and Epidemiology

Journal of Modern Physics, 2011

Research paper thumbnail of An analytic algorithm for the space–time fractional advection–dispersion equation

Computer Physics Communications, 2011

Fractional advection–dispersion equation (FADE) is a generalization of the classical ADE in which... more Fractional advection–dispersion equation (FADE) is a generalization of the classical ADE in which the first order time derivative and first and second order space derivatives are replaced by Caputo derivatives of orders 0<α less-than-or-equals, slant 1, 0<β less-than-or-equals, ...

Research paper thumbnail of A new numerical algorithm to solve fractional differential equations based on operational matrix of generalized hat functions

Communications in Nonlinear Science and Numerical Simulation, 2013

Research paper thumbnail of An analytic algorithm for time fractional nonlinear reaction–diffusion equation based on a new iterative method

Communications in Nonlinear Science and Numerical Simulation, 2012

Research paper thumbnail of Analytic Solution of Fractional-Order Heat- and Wave-Like Equations Using Generalized n -dimensional Differential Transform Method

Zeitschrift für Naturforschung A, 2011

Research paper thumbnail of An analytic solution for the space–time fractional advection–dispersion equation using the optimal homotopy asymptotic method

Computer Physics Communications, 2012

We present an analytic algorithm to solve the space-time fractional advection-dispersion equation... more We present an analytic algorithm to solve the space-time fractional advection-dispersion equation (FADE) based on the optimal homotopy asymptotic method (OHAM), which has the advantage of controlling the region and rate of convergence of the solution series via several auxiliary parameters over the traditional homotopy analysis method (HAM) having only one auxiliary parameter. Furthermore, our proposed algorithm gives better results compared to the Adomian decomposition method (ADM) and the homotopy perturbation method (HPM) in the sense that fewer iterations are required to get a sufficiently accurate solution and the solution has a greater radius of convergence. We find that the iterations obtained by the proposed method converge to the numerical/exact solution of the ADE as the fractional orders α, β, γ tend to their integral values. Numerical examples are given to illustrate the proposed algorithm. The figures and tables show the superiority of the OHAM over the HAM.

Research paper thumbnail of Semi-Analytic Solutions of Electrohydrodynamic Flow in a Circular Cylinder Conduit

Research paper thumbnail of An Efficient Computational Method for the Time-Space Fractional Klein-Gordon Equation

Frontiers in Physics, 2020

Research paper thumbnail of Solution of Electrohydrodynamic Flow Equation Using an Orthogonal Collocation Method Based on Mixed Interpolation

Journal of Applied Mathematics and Physics, 2018

Research paper thumbnail of Semi-analytic algorithms for the electrohydrodynamic flow equation

Journal of Theoretical and Applied Physics, 2012

In this paper, we consider the nonlinear boundary value problem for the electrohydrodynamic (EHD)... more In this paper, we consider the nonlinear boundary value problem for the electrohydrodynamic (EHD) flow of a fluid in an ion-drag configuration in a circular cylindrical conduit. This phenomenon is governed by a nonlinear second-order differential equation. The degree of nonlinearity is determined by a nondimensional parameter α. We present two semi-analytic algorithms to solve the EHD flow equation for various values of relevant parameters based on optimal homotopy asymptotic method (OHAM) and optimal homotopy analysis method. In 1999, Paullet has shown that for large α, the solutions are qualitatively different from those calculated by Mckee in 1997. Both of our solutions obtained by OHAM and optimal homotopy analysis method are qualitatively similar with Paullet’s solutions.

Research paper thumbnail of Generalized Abel Inversion Using Extended Hat Functions Operational Matrix

International Journal of Analysis, 2013

Abel type integral equations play a vital role in the study of compressible flows around axially ... more Abel type integral equations play a vital role in the study of compressible flows around axially symmetric bodies. The relationship between emissivity and the measured intensity, as measured from the outside cylindrically symmetric, optically thin extended radiation source, is given by this equation as well. The aim of the present paper is to propose a stable algorithm for the numerical inversion of the following generalized Abel integral equation:I(y)=a(y)∫αy((rμ-1ε(r))/(yμ-rμ)γ)dr+b(y)∫yβ((rμ-1ε(r)) /(rμ-yμ)γ)dr,α≤y≤β,0<γ<1, using our newly constructed extended hat functions operational matrix of integration, and give an error analysis of the algorithm. The earlier numerical inversions available for the above equation assumed eithera(y)=0orb(y)=0.

Research paper thumbnail of Optimal Variational Asymptotic Method for Nonlinear Fractional Partial Differential Equations

International Scholarly Research Notices, 2014

We propose optimal variational asymptotic method to solve time fractional nonlinear partial diffe... more We propose optimal variational asymptotic method to solve time fractional nonlinear partial differential equations. In the proposed method, an arbitrary number of auxiliary parameters γ0,γ1,γ2,… and auxiliary functions H0(x),H1(x),H2(x),… are introduced in the correction functional of the standard variational iteration method. The optimal values of these parameters are obtained by minimizing the square residual error. To test the method, we apply it to solve two important classes of nonlinear partial differential equations: (1) the fractional advection-diffusion equation with nonlinear source term and (2) the fractional Swift-Hohenberg equation. Only few iterations are required to achieve fairly accurate solutions of both the first and second problems.

Research paper thumbnail of Analytic algorithms for Some Models of Nonlinear Age–Structured Population Dynamics and Epidemiology

Journal of Modern Physics, 2011

Research paper thumbnail of An analytic algorithm for the space–time fractional advection–dispersion equation

Computer Physics Communications, 2011

Fractional advection–dispersion equation (FADE) is a generalization of the classical ADE in which... more Fractional advection–dispersion equation (FADE) is a generalization of the classical ADE in which the first order time derivative and first and second order space derivatives are replaced by Caputo derivatives of orders 0<α less-than-or-equals, slant 1, 0<β less-than-or-equals, ...

Research paper thumbnail of A new numerical algorithm to solve fractional differential equations based on operational matrix of generalized hat functions

Communications in Nonlinear Science and Numerical Simulation, 2013

Research paper thumbnail of An analytic algorithm for time fractional nonlinear reaction–diffusion equation based on a new iterative method

Communications in Nonlinear Science and Numerical Simulation, 2012

Research paper thumbnail of Analytic Solution of Fractional-Order Heat- and Wave-Like Equations Using Generalized n -dimensional Differential Transform Method

Zeitschrift für Naturforschung A, 2011

Research paper thumbnail of An analytic solution for the space–time fractional advection–dispersion equation using the optimal homotopy asymptotic method

Computer Physics Communications, 2012

We present an analytic algorithm to solve the space-time fractional advection-dispersion equation... more We present an analytic algorithm to solve the space-time fractional advection-dispersion equation (FADE) based on the optimal homotopy asymptotic method (OHAM), which has the advantage of controlling the region and rate of convergence of the solution series via several auxiliary parameters over the traditional homotopy analysis method (HAM) having only one auxiliary parameter. Furthermore, our proposed algorithm gives better results compared to the Adomian decomposition method (ADM) and the homotopy perturbation method (HPM) in the sense that fewer iterations are required to get a sufficiently accurate solution and the solution has a greater radius of convergence. We find that the iterations obtained by the proposed method converge to the numerical/exact solution of the ADE as the fractional orders α, β, γ tend to their integral values. Numerical examples are given to illustrate the proposed algorithm. The figures and tables show the superiority of the OHAM over the HAM.