Samala Rathan - Publications

Journal Publications/preprints:

Dispersive PDEs:

Lavanya V Salian, Vivek S Yadav, Rathan Samala, Rakesh Kumar.

Spectral Analysis of Node- and Cell-Centered Higher-Order Compact Schemes for Fully Discrete One and Two Dimensional Convection-Dispersion Equation, [arXiv], Submitted.

Lavanya V Salian, Rathan Samala, Debojyoti Ghosh.

Central compact finite difference scheme with a high spectral resolution for KdV equation,

Numerical Methods for Partial Differential Equations. 42, no. 1 (2026): e70060 [Journal] [SCIE]

Lavanya V Salian, Rathan Samala, Rakesh Kumar.

Compact finite difference scheme for some Sobolev-type equations with Dirichlet boundary conditions,

Journal of Computational Mathematics, 2025 [Journal] [arXiv] [SCIE]

Lavanya V Salian, Rathan Samala.

Exponential approximation space reconstruction weighted essentially nonoscillatory scheme for dispersive partial differential equations.

Mathematical Methods in the Applied Sciences, 47(4), 1823-1851, 2024. [Journal] [arXiv] [SCIE]

Nonlocal Conservation Laws:

Jan Friedrich, Samala Rathan, Sanjibanee Sudha.

A note on the central-upwind scheme for nonlocal conservation laws. [arXiv], Submitted.

Sanjibanee Sudha, Jan Friedrich, Samala Rathan,

Convergence of the non-staggered Nessyahu-Tadmor scheme for coupled systems of one-dimensional nonlocal balance laws, [arXiv], Submitted.

Jan Friedrich, Sanjibanee Sudha, Samala Rathan,

Numerical schemes for a class of nonlocal conservation laws: a general approach,

Networks and Heterogeneous Media, 18(3), 1335-1354, 2023.[Journal] [arXiv] [SCIE]

Relaxation schemes:

Sudipta Sahu, Rathan Samala,

Hydrodynamic limit for discrete velocity kinetic models: A second order semi-implicit central scheme. Submitted.

Sudipta Sahu, Emanuele Macca, Rathan Samala,

Semi-implicit central scheme for hyperbolic systems of balance laws with relaxed source term. [arXiv] Submitted.

Numerical Integration and Time Discretization Schemes:

Shipra Mahata, Rathan Samala.

Explicit Runge-Kutta Methods with MQ and IMQ-Radial Basis Functions,

International Journal of Computational Methods, 2025, [Journal] [arXiv] [SCIE].

Shipra Mahata, Samala Rathan, Juan Ruiz Alverez, Dionisio F Yanez.

A general correction for numerical integration rules over piece-wise continuous functions,

Journal of Computational and Applied Mathematics, Vol. 459, 116378, 2025. [Journal] [SCI]

Samala Rathan, Deepit Shah, T. Hemanth Kumar, K. Sandeep Charan.

Adaptive IQ and IMQ-RBFs for solving initial value problems: Adam-Bashforth and Adam-Moulton methods,

International Journal of Computational Methods, Vol. 21, No. 03, 2350032, 2024. [Journal] [arXiv] [SCIE]

Samala Rathan, Deepit Shah.

Construction and comparative study of second order time stepping methods based on IQ and IMQ-RBFs,

International Journal of Applied and Computational Mathematics, Vol. 8(4), 203, 2022. [Journal] [SCOPUS]

Nonlinear Degenerate PDEs:

Samala Rathan, Jiaxi Gu,

A sixth-order central WENO scheme for nonlinear degenerate parabolic equations,

Computational and Applied Mathematics, 42, 182, 2023.[Journal] [arXiv] [SCIE]

Samala Rathan, Rakesh Kumar, Ameya D. Jagtap.

L1-type smoothness indicators based WENO scheme for nonlinear degenerate parabolic equations,

Applied Mathematics and Computation, Vol.375, 125112, 2020. [Journal] [SCI]

Hamilton-Jacobi Equations:

Samala Rathan, Biswarup Biswas.

Arc Length Based WENO scheme for Hamilton-Jacobi Equations,

Communications on Applied Mathematics and Computation, Vol, 3, 481-496, 2021. [Journal] [SCOPUS, ESCI]

Samala Rathan.

L1-type smoothness indicators based weighted essentially nonoscillatory scheme for Hamilton-Jacobi equations,

International Journal for Numerical Methods in Fluids, Vol, 92(12), 1927-1947, 2020.[Journal] [SCI]

Hyperbolic Conservation Laws:

Samala Rathan, Rakesh Kumar, Lavanya V Salian.

A high-resolution third-order hybrid WENO scheme for solving hyperbolic conservation laws, Submitted.

Arun Govind Neelan, Raimund Bürger, Manoj T. Nair, Samala Rathan.

Higher-order conservative discretizations on arbitrarily varying non-uniform grids.

Computational and Applied Mathematics, Vol .44, Article No. 27, 2025. [Journal] [SCIE]

Samala Rathan, Naga Raju Gande, Ashlesha A. Bhise.

Simple smoothness indicator WENO-Z scheme for hyperbolic conservation laws,

Applied Numerical Mathematics, Vol 157, 255-275, 2020.[Journal] [SCI]

Ashlesha A. Bhise, Naga Raju G, Rathan Samala, Devakar M.

An efficient hybrid weno scheme with a problem independent discontinuity locator,

International Journal for Numerical Methods in Fluids, Vol. 91 (1): 1-28, 2019. [Journal] [SCI]

Samala Rathan, G. Naga Raju.

A modified fifth-order WENO scheme for hyperbolic conservation laws,

Computers and Mathematics with Applications, Vol. 75(5): 1531-1549, 2018. [Journal] [SCI]

Naga Raju Gande, Yogita Rathod, Rathan Samala.

Improved third order weighted essentially non-oscillatory scheme,

International Journal for Numerical Methods in Fluids, Vol. 87: 329–342, 2018. [Journal] [SCI]

Samala Rathan, G. Naga Raju.

Improved weighted ENO scheme based on parameters involved in nonlinear weights,

Applied Mathematics and Computation, Vol. 331: 120-129, 2018. [Journal]. [ SCI]

Naga Raju Gande, Yogita Rathod, Samala Rathan.

Third order WENO scheme with a new smoothness indicator,

International Journal for Numerical Methods in Fluids, Vol. 85: 90–112, 2017. [Journal]. [SCI]

Samala Rathan, G. Naga Raju.

An improved non-linear weights for seventh-order weighted essentially non-oscillatory scheme,

Computers & Fluids, Vol. 156: 496-514, 2017. [Journal] [SCI]

Conference publications:

A. Arun G Neelan, S. Rathan, Triplet Order Adaptive Seventh-Order WENO Scheme for Compressible Flows, Journal of Physics: Conference Series, Volume 2844, 012021, 5th International Conference on Recent Advancement in Physics Sciences, IoP Publishing, 2024. DOI: 10.1088/1742-6596/2844/1/012021

Conference presentations:

A contributed talk on '"A high-resolution third-order hybrid WENO scheme for hyperbolic conservation laws" at the conference HYP2024, Shanghai, China (July 01 -05, 2024)
A contributed talk on '"A high-resolution third-order hybrid WENO scheme for solving hyperbolic conservation laws" at the "Latest Advances in Computational and Applied Mathematics (LACAM-24)" held at IISER Thiruvananthapuram, Kerala, India. (February 21 -24, 2024)
Presented an invited talk titled "High-Resolution Shock Capturing High-order WENO schemes for Hyperbolic Conservation Laws" on 12-10-2018 at IIT Bombay.
Presented an invited talk titled "High-order WENO schemes with variant nonlinear weights for hyperbolic conservation laws" on 25-07-2018 at TIFR CAM, Bangalore.
A contributed talk on “Seventh-order WENO scheme with L1−norm type smoothness indicators” in the Conference on Latest Advances in Computational and Applied Mathematics at Mahindra Ecole Centrale, Hyderabad, December, 15 − 17, 2016.
Presented a contributed talk on "Seventh-order WENO scheme with new smoothness indicators" at the Symposium on Mathematics and its Applications (Dec 22-2016) organized by the Department of Mathematics, VNIT, Nagpur.
Selected for contributed paper in Conference on Computational PDE 2015 at TIFR CAM, Bengaluru titled " Investigation of weighted essentially non-oscillatory scheme at critical points and near discontinuities".

InvitedTalks/Lectures at workshops:

Presented an invited talk titled "Semi-implicit central scheme for hyperbolic systems of balance laws with relaxed source term" in the 5th international conference on Mathematical Modelling, Computational Intelligence Techniques and Renewable Energy (MMCITRE-2025) at SPM IIIT Naya Raipur, Chhattisgarh(10-12, Dec-2025)
Presented an invited talk titled "Hybridization of a third-order WENO for solving hyperbolic conservation laws" at the Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Germany(17-06-2025).
Presented an invited talk titled "Hybridization of a third-order WENO for solving hyperbolic conservation laws" at School of Business Informatics and Mathematics, University of Mannheim, Germany(27-05-2025).
Presented an invited talk titled "Hybrid WENO for solving hyperbolic conservation laws" at Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, Germany(14-07-2025)
Presented an invited talk titled "A high-resolution third-order hybrid weighted essentially nonoscillatory scheme for hyperbolic conservation laws" in the International Conference on Connecting Theory and Practice in Mathematics, Statistics and Data Science (ICMSD-2025) during 15-17, March 2025 organized by the Department of Mathematics, School of Advanced Sciences, VIT-AP University and Department of Mathematics and Statistics, The University of the West Indies, Trinidad and Tobago.
Presented an invited talk titled "High-Resolution Third-Order Hybrid WENO Scheme for Hyperbolic Conservation Laws" in the 12th National Conference on Mathematical Techniques and Applications (NCMTA-2025) during 09-10, January 2025 organized by the Department of Mathematics, SRMIST Chennai, Tamilnadu, India.
Speaker in NCM ATM workshop on "Numerical Methods for Partial Differential Equations" during December 16-27, 2024, held at IIPE, Visakhapatnam, India.
Presented an invited talk titled "Numerical methods for scalar hyperbolic conservation laws" in the workshop on 'Recent Advances in Differential Equations and Applications' organized by the Department of Mathematics, School of Advanced Sciences, VIT AP University, Andhra Pradesh, India, 27th October 2023.
"Numerical methods for scalar hyperbolic conservation laws" in the workshop on 'Recent Advances in Differential Equations and Applications' organized by the Department of Mathematics, School of Advanced Sciences, VIT AP University, Andhra Pradesh, India, 27th October 2023.

Workshops/Conferences/Short_Courses:

Local organizer, "NCM ATM workshop on Numerical Methods for Partial Differential Equations," December 16-27, 2024, IIPE, Visakhapatnam, India.

Convener, "Shortcourse in Applications of Scalar Hyperbolic Conservation Laws," March 1-5, 2024, IIPE, Visakhapatnam, India.

Treasurer, A four-day workshop on "Research Opportunities in Petroleum, Energy and Natural Gas (ReOPEN)," Feb 24-27, 2020, IIPE, Visakhapatnam, India.

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