Jyoti Talwar

A new spline in compression approximation for one space dimensional quasilinear parabolic equations on a variable mesh

In this paper, we propose a new two level implicit method of order two in time and four in space directions, based on spline in compression approximation for the numerical solution of one space dimensional quasi-linear parabolic partial differential equation on a uniform mesh. The derivation and the stability of the proposed method are discussed in details. We have extended the method to non-uniform mesh. Numerical results are given to illustrate the usefulness of the proposed method.

A new algorithm based on spline in tension approximation for 1D quasi-linear parabolic equations on a variable mesh

In this paper, we propose a new two-level implicit method of order two in time and four in space directions, based on spline in tension approximation for the numerical solution of one space dimensional quasi-linear parabolic partial differential equation on a uniform mesh. We have discussed the derivation of the proposed method in detail and have also discussed the stability analysis for a model problem. We have extended the method to non-uniform mesh. Numerical results are given to illustrate the usefulness of the proposed methods.

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

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.

A new compact alternating group explicit iteration method for the solution of nonlinear time-dependent viscous Burgers’ equation

We discuss a new single-sweep compact alternating group explicit method for solving the time-dependent viscous Burgers’ equation both in Cartesian and polar coordinates. An error analysis for the new iterative method is discussed in detail.We compared the results of the proposed iterative method with the results of a corresponding double-sweep alternating group explicit (AGE) iterative method to demonstrate computationally the efficiency of the proposed method.

A new coupled reduced alternating group explicit method for nonlinear singular two-point boundary value problems on a variable mesh

In this paper, we discuss a new coupled reduced alternating group explicit (CRAGE) and Newton-CRAGE iteration methods to solve the nonlinear singular two-point boundary value problems u″ = f(r, u, u′), 0 < r < 1 subject to given natural boundary conditions u(0) = A1, u(1) = A2 where A1 and A2 are finite constants, along with a third-order numerical method on a geometric mesh. The proposed method is applicable to singular and nonsingular problems. We have discussed the convergence of the CRAGE iteration method in detail. The results obtained from the proposed CRAGE iteration method are compared with the results of the corresponding two-parameter alternating group explicit (TAGE) iteration methods to demonstrate computationally the efficiency of the proposed method.

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

In this paper, 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 nonlinear viscous Burgers’ equation subject to given natural boundary conditions. The proposed method is also applicable to both singular and non-singular problems, which is main attraction of our work. The convergence of the proposed method is discussed in detail. We compared the results of proposed iteration method with the results of corresponding double sweep alternating group explicit iteration method to demonstrate computationally the efficiency of the proposed method.

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

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 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.