Venu Gopal

Brown University, Division of Applied Mathematics, Post-Doc

University of Delhi, Mathematics, Alumnus

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Supervisors: Chi-Wang Shu and Ranjan K Mohanty
Phone: 001-401-863-1413
Address: 182, George Street
Division of Applied Mathematics
Brown University
Providence
Rhode Island 02912

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Judith L Green

University of California, Santa Barbara

David Seamon

Kansas State University

Petko Kiriazov

Bulgarian Academy of Sciences

Adnene TLILI

ISET Nabeul

Lev Manovich

Graduate Center of the City University of New York

Andrea Di Rosa

University of Haifa

pablo barrera

UNAM Universidad Nacional Autónoma de México

Gal Kirn

Filozofska Fakulteta Ljubljana

Heron Surbakti

Universitas Sriwijaya

Sergey Konovalov

Russian Academy of Sciences 1

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Papers by Venu Gopal

New Non-polynomial Spline in Compression Method of O(k2+h4) for the solution of 1D Wave equation in Polar co-ordinates

A Fourth Order Finite Difference Method based on Spline in Tension Approximation for the Solution of One-space Dimensional Second Order Quasi-linear Hyperbolic Equation

In this paper, we propose a new three-level implicit nine-point compact finite difference formula... more In this paper, we propose a new three-level implicit nine-point compact finite difference formulation of order two in time and four in space directions, based on spline in tension approximation in x-direction and central finite difference approximation in t-direction for the numerical solution of one-space dimensional second-order quasi-linear hyperbolic equations with first-order space derivative term. We describe the mathematical formulation procedure in detail and also discuss how our formulation is able to handle a wave equation in polar coordinates. The proposed method, when applied to a general form of the telegrapher equation, is also shown to be unconditionally stable. Numerical examples are used to illustrate the usefulness of the proposed method. MSC: 65M06; 65M12

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A New High Accuracy Non-polynomial Tension Spline Method for the Solution of One Dimensional Wave Equation in Polar Co-ordinates

An off-step discretization for the solution of 1-D mildly non-linear wave equations with variable coefficients

i-asr.com

In this paper, we propose a new three-level implicit scheme of O(k 2 + k 2 h 2 +h 4 ) based on of... more In this paper, we propose a new three-level implicit scheme of O(k 2 + k 2 h 2 +h 4 ) based on off-step discretization for the solution of 1-D non-linear hyperbolic partial differential equation of the form u tt = A(x, t)u xx + ϕ(x, t, u, u x , u t ), 0 < x < 1, t > 0 subject to appropriate initial and Dirichlet boundary conditions, where k > 0 and h > 0 are mesh sizes in time and space dimensions respectively. We require only 9-grid points and a single computational cell. The proposed method is directly applicable to hyperbolic equations in polar coordinates, which is main advantages of our work. We do not require any special technique to handle singular coefficients of the differential equation. We describe the derivation procedure in details. The proposed method is shown to be unconditionally stable when applied to a linear hyperbolic equation. Numerical results illustrate the fourth order convergence of the proposed method.

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HIGH ACCURACY ARITHMETIC AVERAGE TYPE DISCRETIZATION FOR THE SOLUTION OF TWO-SPACE DIMENSIONAL NONLINEAR WAVE EQUATIONS

International Journal of Modeling Simulation and Scientific Computing, Jan 1, 2012

In this paper, we propose a new high accuracy discretization based on the ideas given by Chawla a... more In this paper, we propose a new high accuracy discretization based on the ideas given by Chawla and Shivakumar for the solution of two-space dimensional nonlinear hyperbolic partial differential equation of the form utt = A(x, y, t)uxx + B(x, y, t)uyy + g (x, y, t, u, ux, uy, ut), 0 < x, y < 1, t > 0 subject to appropriate initial and Dirichlet boundary conditions. We use only five evaluations of the function g and do not require any fictitious points to discretize the differential equation. The proposed method is directly applicable to wave equation in polar coordinates and when applied to a linear telegraphic hyperbolic equation is shown to be unconditionally stable. Numerical results are provided to illustrate the usefulness of the proposed method. Int. J. Model. Simul. Sci. Comput. 2012.03. Downloaded from www.worldscientific.com by BROWN UNIVERSITY on 07/26/13. For personal use only. 1150005-2 Int. J. Model. Simul. Sci. Comput. 2012.03. Downloaded from www.worldscientific.com by BROWN UNIVERSITY on 07/26/13. For personal use only.

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A New Off-step High Order Approximation for the Solution of Three-space Dimensional Nonlinear Wave Equations

Applied Mathematical Modelling, Jan 1, 2013

In this paper, we propose a new high accuracy numerical method of O(k 2 + k 2 h 2 + h 4 ) based o... more In this paper, we propose a new high accuracy numerical method of O(k 2 + k 2 h 2 + h 4 ) based on off-step discretization for the solution of 3-space dimensional non-linear wave equation of the form u tt = A(x,y,z,t)u xx + B(x,y,z,t)u yy + C(x,y,z,t)u zz + g(x,y,z,t,u,u x ,u y ,u z ,u t ), 0 < x,y,z < 1,t > 0 subject to given appropriate initial and Dirichlet boundary conditions, where k > 0 and h > 0 are mesh sizes in time and space directions respectively. We use only seven evaluations of the function g as compared to nine evaluations of the same function discussed in [3,4]. We describe the derivation procedure in details of the algorithm. The proposed numerical algorithm is directly applicable to wave equation in polar coordinates and we do not require any fictitious points to discretize the differential equation. The proposed method when applied to a telegraphic equation is also shown to be unconditionally stable. Comparative numerical results are provided to justify the usefulness of the proposed method.

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High accuracy cubic spline finite difference approximation for the solution of one-space dimensional non-linear wave equations

Applied Mathematics and Computation, Nov 1, 2011

In this paper, we propose a new three-level implicit nine point compact cubic spline finite diffe... more In this paper, we propose a new three-level implicit nine point compact cubic spline finite difference formulation of order two in time and four in space directions, based on cubic spline approximation in x-direction and finite difference approximation in t-direction for the numerical solution of one-space dimensional second order non-linear hyperbolic partial differential equations. We describe the mathematical formulation procedure in details and also discuss how our formulation is able to handle wave equation in polar coordinates. The proposed method when applied to a linear hyperbolic equation is also shown to be unconditionally stable. Numerical results are provided to justify the usefulness of the proposed method. j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / a m c

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A New Spline Approximation for the Solution of One-space Dimensional Second Order Non-linear Wave Equations With Variable Coefficients

In this paper, we propose a new three-level implicit nine point compact finite difference formula... more In this paper, we propose a new three-level implicit nine point compact finite difference formulation of order two in time and four in space directions, based on non-polynomial spline in compression for the solution of one-space dimensional second order non-linear hyperbolic partial differential equations with variable coefficients and significant first order space derivative term. We describe the Mathematical formulation procedure in details and also discussed the stability. Numerical results are provided to justify the usefulness of the proposed method.

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New Non-polynomial Spline in Compression Method of O(k2+h4) for the solution of 1D Wave equation in Polar co-ordinates

A Fourth Order Finite Difference Method based on Spline in Tension Approximation for the Solution of One-space Dimensional Second Order Quasi-linear Hyperbolic Equation

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A New High Accuracy Non-polynomial Tension Spline Method for the Solution of One Dimensional Wave Equation in Polar Co-ordinates

An off-step discretization for the solution of 1-D mildly non-linear wave equations with variable coefficients

i-asr.com

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HIGH ACCURACY ARITHMETIC AVERAGE TYPE DISCRETIZATION FOR THE SOLUTION OF TWO-SPACE DIMENSIONAL NONLINEAR WAVE EQUATIONS

International Journal of Modeling Simulation and Scientific Computing, Jan 1, 2012

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A New Off-step High Order Approximation for the Solution of Three-space Dimensional Nonlinear Wave Equations