Publications

Higher-Order Numerical Schemes for Hyperbolic Conservation Laws:

1. 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]

2. 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]

3. 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]

4. 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]

5. 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] 

6.  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]

7. 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]

Higher-Order Numerical Schemes for Nonlinear Degenerate Parabolic PDEs:

8. 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]

9. 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] 

Higher-Order Numerical Schemes for Hamilton-Jacobi Equations:

10. 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]

11. 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]

Numerical Schemes for Nonlocal Conservation Laws:

12. 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] 

Numerical Schemes for Dispersive PDEs:

13. Lavanya V Salian, Samala Rathan.

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]

Time-Discretization Schemes:

14. 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]

15. 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]

Conference presentations:

1. Samala Rathan, Rakesh Kumar: 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)" will be held at IISER Thiruvananthapuram, Kerala, India. (February 21 -24, 2024) 

2. Lavanya V Salian, Samala Rathan, Debojyoti Ghosh: A contributed talk on '"A new central compact finite difference scheme with high spectral resolution for dispersive equations" at the "Latest Advances in Computational and Applied Mathematics (LACAM-24)" will be held at IISER Thiruvananthapuram, Kerala, India.  (February 21 -24, 2024)   [Best presentation award to Lavanya V Salian]

3. Jan Friedrich, Sanjibanee Sudha, Samala Rathan: Selected a paper (abstract) titled "Numerical methods for nonlocal conservation laws" at the "89th Annual Conference on Indian Mathematical Society (IMS)" organized by the Department of Mathematics, BITS PILANI Hyderabad (Dec 22-27, 2023)  

4. Lavanya V. Salian, Samala Rathan: Selected a paper (abstract)  titled " "A fifth-order WENO scheme with exponential basis for solving dispersive equations" to present at the  "International Conference on Applied Mathematics and Mechanics (ICAMM 2023)" organized by Department of Mathematics, IIT Indore (October 18-20, 2023) 

5. Lavanya V. Salian, Samala Rathan: Selected a paper (abstract)  titled " "Weighted essentially non-oscillatory scheme for dispersion equations with exponential approximation space" to present at the  "International Conference on Differential Equations and Control Problems (ICDECP23)'" organized by the Department of Mathematics & Statistics, IIT Mandi (June 15-17, 2023) 

6. Arun Govind Neelan, Samala Rathan: Selected a paper (abstract) titled "Numerical stability analysis using deep neural network" to present at the  "International Conference on Differential Equations and Control Problems (ICDECP23)'" organized by the Department of Mathematics & Statistics, IIT Mandi(June 15-17, 2023) 

7. Sudipta Sahu, Samala Rathan: Selected a paper (abstract) titled "Improved upwind scheme for advection equation with exponential approximation space"  to present at the "International Conference on Differential Equations and Control Problems (ICDECP23)'" organized by the Department of Mathematics & Statistics, IIT Mandi (June 15-17, 2023) 

8. Jan Friedrich, Sanjibanee Sudha, Samala Rathan: Selected a paper (abstract) titled “Finite-volume schemes for a class of non-local conservation laws" to present at the "International Conference on Differential Equations and Control Problems (ICDECP23)'" organized by the Department of Mathematics & Statistics, IIT Mandi (June 15-17, 2023) 

9. Sudipta Sahu, Samala Rathan: Selected an abstract titled "Improved upwind scheme for advection equation with exponential approximation space" as a contributed talk at the 'Second International Conference on Mathematical Analysis and Computing (ICMAC-2022)' held at SSN College of Engineering, Tamilnadu (Dec 22-23, 2022) 

10. Presented an invited talk titled "High-Resolution Shock Capturing High-order WENO schemes for Hyperbolic Conservation Laws" on 12-10-2018 at IIT Bombay. 

11. 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. 

12. 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.

13. 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.

14. 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".

Talks/Lectures:

1. "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. [Lecture Slides]