R. K. Mohanty

South Asian University

Author Statistics

Papers

Citation

H-Index

i-10 index

Research Field

An Unconditionally Stable ADI Method for the Linear Hyperbolic Equation in Three Space Dimensions

International Journal of Computer Mathematics (2002)

R. K. Mohanty Manoj Jain Urvashi Arora

An unconditionally stable alternating direction implicit (ADI) method of O(k 2 +h 2 ) of Lees type for solving the three space dimensional linear hyperbolic equation u tt +2 f u t + g 2 u = u xx + u yy + u zz + f ( x , y , z , t ), 00 subject to appropriate initial and Dirichlet boundary conditions is proposed, where f >0 and g S 0 are real numbers. For this method, we use a single computational cell. The resulting system of algebraic equations is solved by three step split method. The new method is demonstrated by a suitable numerical example.

Algebraic equation

Linear equation

10.1080/00207160211918

Cite

Citations (97)

On the Convergence of Non-Polynomial Spline Finite Difference Method for Quasi-Linear Elliptic Boundary Value Problems in Two-Space Dimensions

Journal of Advances in Applied Mathematics (2016)

Navnit Jha Ravindra Kumar R. K. Mohanty

An approximate solution technique based on non-polynomial spline and finite difference method has been described for two-space dimensional quasi-linear elliptic boundary value problems.The numerical scheme in the limiting case of non-polynomial spline parameter provides the cubic spline scheme.The proposed scheme is analyzed for the convergence using matrix theory.Experimental results show the importance of using non-polynomial spline scheme over corresponding cubic spline scheme in terms of iterations to achieve desired accuracy.The method is tested for the convergence and corroborates the theoretical truncation errors.The accuracy in the solutions is obtained for Tricomi and Khokhlov-Zabolotskaya equations for various mesh step sizes.

Spline (mechanical)

Perfect spline

Hermite spline

M-spline

Finite difference

10.22606/jaam.2016.11006

Cite

Citations (1)

A Combined Arithmetic Average Discretization and TAGE Iterative Method for Non-linear Two Point Boundary Value Problems with a Source Function in Integral Form

Differential Equations and Dynamical Systems (2012)

R. K. Mohanty

10.1007/s12591-012-0140-8

Cite

Citations (3)

A New Compact Off-Step Discretization for the System of 2D Quasi-Linear Elliptic Equations on Unequal Mesh

Computational Mathematics and Modeling (2014)

R. K. Mohanty Nikita Setia

Compact finite difference

Finite difference

10.1007/s10598-014-9234-1

Cite

Citations (3)

Three point discretization of order four and six for (du:dx) of the solution of non-linear singular two point boundary value problem

International Journal of Computer Mathematics (2001)

R. K. Mohanty David J. Evans Shivani Dey

Abstract We present finite difference methods of order four and six for the numerical solution of (du/dx) for the non-linear differential equation u″ = f(x,u,u′), 0 < x > 1 subject to the boundary conditions u(0) = A, u(l) =B. The proposed methods require only three grid points and applicable to both singular and non-singular problems. Numerical examples are given to illustrate the methods and their convergence. Keywords: Finite difference methodsNon-linear equationLocal truncation errorSingular equationFirst order derivativeBurger's equationRMS errorsC.R. Categories: G.1.7 Corresponding author Corresponding author Notes Corresponding author

Truncation error

Singular value

Singular solution

Truncation (statistics)

10.1080/00207160108805101

Cite

Citations (8)

Third order accurate variable mesh discretization and application of TAGE iterative method for the non-linear two-point boundary value problems with homogeneous functions in integral form

Applied Mathematics and Computation (2009)

R. K. Mohanty Deepika Dhall

10.1016/j.amc.2009.07.046

Cite

Citations (8)

A Single Sweep AGE Algorithm on a Variable Mesh Based on Off-Step Discretization for the Solution of Nonlinear Burgers’ Equation

Journal of Computational Methods in Physics (2014)

R. K. Mohanty Jyoti Talwar

We discuss a new single sweep alternating group explicit iteration method, along with a third-order numerical method based on off-step discretization on a variable mesh to solve the nonlinear ordinary differential equation y′′=f(x,y,y′) subject to given natural boundary conditions. Using the proposed method, we have solved Burgers’ equation both in singular and nonsingular cases, which is the main attraction of our work. The convergence of the proposed method is discussed in detail. We compared the results of the proposed iteration method with the results of the corresponding double sweep alternating group explicit iteration methods to demonstrate computationally the efficiency of the proposed method.

10.1155/2014/853198

Cite

Citations (0)

Application of TAGE Iterative Methods for the Solution of Nonlinear Two Point Boundary Value Problems with Linear Mixed Boundary Conditions on a Non-Uniform Mesh

International Journal for Computational Methods in Engineering Science and Mechanics (2012)

R. K. Mohanty Jyoti Talwar Noopur Khosla

We report the application of two parameter alternating group explicit (TAGE) iteration and Newton-TAGE iteration methods for the solution of nonlinear differential equation u″=F(x, u, u′) subject to linear mixed boundary conditions on a non-uniform mesh. In both cases, we use only three non-uniform grid points. The convergence theory for TAGE iteration method is analyzed. Numerical examples are considered to demonstrate computationally and the utility of TAGE iteration methods.

10.1080/15502287.2012.660228

Cite

Citations (3)

A new stable variable mesh method for 1-D non-linear parabolic partial differential equations

Applied Mathematics and Computation (2006)

Urvashi Arora Samir Karaa R. K. Mohanty

10.1016/j.amc.2006.02.032

Cite

Citations (9)

A Higher Order Finite Difference Method for Numerical Solution of the Kuramoto–Sivashinsky Equation

Springer proceedings in mathematics & statistics (2020)

Deepti Kaur R. K. Mohanty