Publications

Prof. Gujji Murali Mohan Reddy

Associate Professor,
Department of Mathematics

A priori and a posteriori error analysis, Evolution Problems with Memory, Inverse problems, Numerical Analysis, Numerical methods to PDEs, Stochastic PDEs

Journal Publications (by area):

Adaptive FEM

N. Shravani, G. M. M. Reddy and M. Vynnycky, A posteriori error estimates for the Crank-Nicolson method: application to parabolic partial differential equations with small random input data, J. Sci. Comput., pp. 1-36, 104(2025), Springer.
N. Shravani, G. M. M. Reddy and Amiya K. Pani, Anisotropic a posteriori error analysis for the two-step backward differentiation formula for parabolic integro-differential equation, J. Sci. Comput., pp. 1-26, 93(2022), Springer.
G. M. M. Reddy, Fully discrete a posteriori error estimates for parabolic integro-differential equations using two-step backward differentiation formula, BIT Numer. Math., pp. 251-277, 62(2022),Springer.
G. M. M. Reddy, R. K. Sinha and J.A. Cuminato, A posteriori error analysis of Crank-Nicolson finite element method for parabolic integro-differential equations, J. Sci. Comput., pp. 414–441, 79(2019), Springer.
J. S. Gupta, R. K. Sinha, G. M. M. Reddy and J. Jain, A posteriori error analysis of the Crank-Nicolson finite element method for linear parabolic interface problems: A reconstruction approach, J. Comput. Appl. Math., pp.173–190, 340(2018), Elsevier.
J. S. Gupta, R. K. Sinha, G. M. M. Reddy and J. Jain, New Clement type interpolation inequalities and a posteriori error estimates for linear parabolic interface problems, Numer. Methods Partial Diffe. Equations, pp. 570–598, 33(2017), Wiley.
J. S. Gupta, R. K. Sinha, G. M. M. Reddy and J. Jain, A posteriori error analysis of two-step backward differentiation formula finite element approximation for parabolic interface problems, Journal of Scientific Computing, pp. 406–429, 69(2016), Springer.
G. M. M. Reddy and R. K. Sinha, On the Crank-Nicolson anisotropic a posteriori error analysis for parabolic integro-differential equations, Math. Comp., pp. 2365–2390, 85(2016), American Mathematical Society.
G. M. M. Reddy and R. K. Sinha, The backward Euler anisotropic a posteriori error analysis for parabolic integro-differential equations, Numer. Methods Partial Differential Equations, pp. 1309–1330, 32(2016), Wiley.
G. M. M. Reddy and R. K. Sinha, Ritz-Volterra reconstructions and a posteriori error analysis of finite element method for parabolic integro-differential equations, IMA J. Numer. Anal., pp. 341–371, 35(2015), Oxford Journals.

Inverse Problems

P. Nanda, G. M. M. Reddy, and M. Vynnycky, An inverse two-phase nonlinear Stefan problem: a phase-wise split approach, Comput. Math. with Appl., accepted for publication.
P. Nanda, and G. M. M. Reddy, Efficient numerical solution of one-phase inverse Stefan problem in two-dimensions: a posteriori error control, Stud. Appl. Math., pp. 1563–1585, 148(2022).
G. M. M. Reddy, P. Nanda, M. Vynnycky and J.A. Cuminato, Efficient numerical solution of boundary identification problems: MFS with adaptive stochastic optimization, Applied Mathematics and Computation, 409, 12640 (2021), Elsevier.
G. M. M. Reddy, P. Nanda, M. Vynnycky and J.A. Cuminato, An adaptive boundary algorithm for the reconstruction of boundary and initial data using the method of fundamental solutions for the inverse Cauchy-Stefan problem, Computational and Applied Mathematics, pp. 1–26, 40(2021), Springer.
G. M. M. Reddy, M. Vynnycky and J.A. Cuminato, An efficient adaptive boundary algorithm to reconstruct Neumann boundary data in the MFS for the inverse Stefan problem, Journal of Computational and Applied Mathematics, pp.21–40, 349(2019), Elsevier.
G. M. M. Reddy, M. Vynnycky and J.A. Cuminato, On efficient reconstruction of boundary data with optimal placement of the source points in the MFS: application to inverse Stefan problems, Inverse Problems in Science and Engineering, pp. 1249–1279, 26(2018), Taylor & Francis.

Others

G. M. M. Reddy, A. B. Seitenfuss, D. O. Medeiros, L. Meacci, M. Assunção and M. Vynnycky, A Compact FEM Implementation for Parabolic Integro-Differential Equations in 2D, Algorithms, pp. 1-24, 13(2020). (Documentation for the software is available in the software section)
M. Vynnycky and G. M. M. Reddy, On the effect of control-point spacing on the multisolution phenomenon in the P3P problem, Mathematical Problems in Engineering, pp. 13, 2018(2018), Hindawi.

Software

DOCUMENTATION: A Compact FEM Implementation for Parabolic Integro-Differential Equations in 2D/uploads/algorithms-13-00242.pdf

SOFTWARE ARCHIEVE: https://github.com/LucaMeacci/efficient-PIDE-2D

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