Research Interests:
Broad Area: Applied Mathematics
Numerical Schemes for Hyperbolic Balance Laws and Related Models
Numerical methods for Dispersive PDEs and its hyperbolization
Nonlocal conservation laws: Applications to traffic flows
Finite Difference and Finite Volume methods
Weighted Essentially Non-Oscillatory (WENO) schemes
Implicit-Explicit schemes, Relaxation schemes
Preprints:
Sudipta Sahu, Emanuele Macca, Rathan Samala,
Semi-implicit central scheme for hyperbolic systems of balance laws with relaxed source term.[arXiv] Submitted
Sudipta Sahu, Rathan Samala,
Hydrodynamic limit for discrete velocity kinetic models: A second order semi-implicit central scheme. Submitted
Sudipta Sahu, Rathan Samala.
Numerical Scheme to Vasudeva Murthy's Alternative Relaxation Approach for Hyperbolic Balance Laws. Submitted
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
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
Jiaxi Gu, Samala Rathan.
Finite Difference WENO scheme by exponential approximation space for nonlinear degenerate parabolic equations, In preparation
Samala Rathan, LxW type time discretization scheme for hyperbolic conservation laws, In preparation
Samala Rathan, Rakesh Kumar, Lavanya V Salian.
Third-order hybrid WENO scheme for solving hyperbolic conservation laws. In preparation
Journal Publications:
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]
Shipra Mahata, Rathan Samala.
Explicit Runge-Kutta Methods with MQ and IMQ-Radial Basis Functions,
International Journal of Computational Methods, 2026, [Journal] [arXiv] [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]
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]
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]
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]
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]
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]
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, 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]
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]
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]
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
Completed Projects:
Title of the project: Design and development of numerical scheme for nonlocal conservation laws in multi-dimension,
Sponsoring agency: PECFAR-IGSTC, (Paired Early Career Fellowship in Applied Research, Indo-German Science & Technology Centre),
Co-PI: Dr. Jan Friedrich,
Duration: Feb-June, 2025.
Total Project: Rs. 7,26,658.00/-
2. Title of the project: Design and Development of Numerical Schemes for Hyperbolic Systems of Conservation Laws
Sponsoring agency: NBHM, DAE
Total budget: Rs. 18,31,794.00/-
Project duration: 3 years (Dec, 2021-Feb, 2025.)
3. Title of the project: Design and Analysis of Numerical Techniques for Hyperbolic Systems of Conservation Laws
Sponsoring agency: IRG, IIPE Visakhapatnam
Total budget: Rs. 8,31,070.00/-
Project duration: 3 years (June, 2021-June, 2024)
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.
Workshop/conference participation:
Participated in "National Conference on Computational Mathematics" held at NIT Puducherry, Karaikal, 22-23 Dec, 2022.
Participated in ICERM workshop on Holistic Design of Time-Dependent PDE discretizations, Jan 10-14, 2022
Participated in ICERM workshop on Advances and challenges in Hyperbolic Conservation Laws, May 17-21, 2021
Participated in a symposium titled "Symposium on Conservation Laws and Related Topics" held on 31st July 2020 in honor of Prof. G.D. Veerappa Gowda, conducted by TIFR-CAM, Bangalore, India.
Participated in five-day FDP on topic titled "Introduction to Machine Learning using Python" held from 11th-12th and 18th-20th July 2020 conducted by Soft Computing Research Society, New Delhi, India.
Participated in Diamond Jubilee Symposium, Department of Mathematics-2019 organized by Department of Mathematics, IIT Bombay (04 Jan 2019-06 Jan 2019).
Participated in Symposium on Mathematics and its Applications (Dec 22-2017) organized by Department of Mathematics, VNIT, Nagpur.
Attended a workshop on "Numerical Techniques for Partial Differential Equations (10th July-14th July 2017)" organized by Department of Mathematics, VNIT, Nagpur.
Attended Advanced Training in Mathematics (ATM) School: AIS Linear Partial Differential Equations (19th July-8th July, 2017) held at TIFR-CAM, Bangalore.
Actively Participated as a volunteer in 81st annual conference of The Indian Mathematical Society (Dec 27-30, 2015) at VNIT, Nagpur.
Attended the NPDE-TCA postgraduate level training program on differential equations (25 May-14 June, 2015) at BITS-Pilani, Goa.
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.
Professional Activities(As a reviewer):
Mathematical Reviews (Americal Mathematical Society)
Applied Numerical Mathematics (Elsevier )
Acta Mechanica Sinica (Springer)
Computers & Fluids (Elsevier )
European Journal of Mechanics/B Fluids (Elsevier)
Results in Applied Mathematics (Elsevier)
International Journal for Numerical Methods in Fluids (Wiley )
International Journal of Computer Mathematics (Taylor & Francis)
International Journal of Computational Fluid Dynamics (Taylor & Francis)
Computational and Applied Mathematics (Springer)
Communications in Nonlinear Science and Numerical Simulation (Elsevier )
Indian Journal of Pure and Applied Mathematics (Springer)
Journal of Applied Mathematics (Hindwavi)
zbMath Open
Journal of Computational Physics (Elsevier)
Journal of Computational Science (Elsevier)
Journal of Computational and Applied Mathematics (Elsevier)
Computers and Mathematics with Applications (Elsevier)
International Journal for Computational Methods in Engineering Science & Mechanics (Taylor & Francis)
