PUBLICATIONS (Journal Articles):

Aayushman Raina, Satyadev Badireddi, S. Natesan, Application of PINN to Obtain Solution of Boundary Layer Problems Arising in Fluid Dynamics, Mathematical Foundations of Computing, (In Press). 

Aayushman Raina, S. Natesan, Suayip Toprakseven, An Efficient Operator Splitting Weak Galerkin Method for Singularly Perturbed 2D Parabolic PDEs , Numerical Algorithms (In Press). 

Aayushman Raina, S. Natesan, A Weak Galerkin Finite Element method for Fourth order Parabolic Singularly Perturbed Problems on layer adapted Shishkin mesh, Applied Numerical Mathematics, 207 (2025), pp.~520--533. (Elsevier, SCIE, IF: 2.2)

DOI: https://doi.org/10.1016/j.apnum.2024.09.019 

Aayushman Raina, S. Natesan, Suayip Toprakseven, Anisotropic Error Analysis of Weak Galerkin finite element method for Singularly Perturbed Biharmonic Problems, Mathematics and Computers in Simulation, 229 (2025), pp.~203--221. (Elsevier, SCIE, IF: 4.4)

DOI: doi.org/10.1016/j.matcom.2024.09.017 

Aayushman Raina, S. Natesan, Suayip Toprakseven, A Novel ADI-Weak Galerkin Method for Singularly Perturbed Two-Parameter 2D Parabolic PDEs, Numerical Methods for Partial Differential Equations, 41 (2025), p.~e23169. (John Wiley and Sons Inc, SCIE, IF: 2.1)

DOI: doi.org/10.1002/num.23169  

Arxiv Preprint(s)

Pradanya Boro, Aayushman Raina, S. Natesan, A Parameter-Driven Physics-Informed Neural Network Framework for Solving Two-Parameter Singular Perturbation Problems Involving Boundary Layers, arXiv:2505.01159 (2025), https://doi.org/10.48550/arXiv.2505.01159