Experiments with MRAI Time Stepping Schemes on a Distributed Memory Parallel Environment. - Mikhail A. Botchev (HPCN Europe, 1998)

Testing Weighted Splitting Schemes on a One-Column Transport-Chemistry Model. - Mike A. Botchev; István Faragó; Ágnes Havasi (LSSC, 2003)

The Gautschi time stepping scheme for edge finite element discretizations of the Maxwell equations. - Mike A. Botchev; Davit Harutyunyan; Jaap J. W. van der Vegt (J. Comput. Phys., 2006)

A Class of Nonsymmetric Preconditioners for Saddle Point Problems. - Mike A. Botchev; Gene H. Golub (SIAM J. Matrix Anal. Appl., 2006)

Dispersion and Dissipation Error in High-Order Runge-Kutta Discontinuous Galerkin Discretisations of the Maxwell Equations. - D. Sármány; Mike A. Botchev; Jaap J. W. van der Vegt (J. Sci. Comput., 2007)

Multilevel iterative solvers for the edge finite element solution of the 3D Maxwell equation. - Oleg V. Nechaev; Ella P. Shurina; Mike A. Botchev (Comput. Math. Appl., 2008)

Numerical Integration of Damped Maxwell Equations. - Mike A. Botchev; Jan G. Verwer (SIAM J. Sci. Comput., 2009)

Block Krylov subspace exact time integration of linear ODE systems. Part 1: algorithm description - Mikhail A. Botchev (CoRR, 2011)

Residual, restarting and Richardson iteration for the matrix exponential, revised - Mike A. Botchev (CoRR, 2011)

Time-integration methods for finite element discretisations of the second-order Maxwell equation. - D. Sármány; Mike A. Botchev; Jaap J. W. van der Vegt (Comput. Math. Appl., 2013)

A block Krylov subspace time-exact solution method for linear ordinary differential equation systems. - Mike A. Botchev (Numer. Linear Algebra Appl., 2013)

Residual, Restarting, and Richardson Iteration for the Matrix Exponential. - Mike A. Botchev; Volker Grimm; Marlis Hochbruck (SIAM J. Sci. Comput., 2013)

Iterative across-time solution of linear differential equations: Krylov subspace versus waveform relaxation. - Mike A. Botchev; Ivan V. Oseledets; Eugene E. Tyrtyshnikov (Comput. Math. Appl., 2014)

Krylov subspace exponential time domain solution of Maxwell's equations in photonic crystal modeling. - Mikhail A. Botchev (J. Comput. Appl. Math., 2016)

A block Krylov subspace implementation of the time-parallel Paraexp method and its extension for nonlinear partial differential equations. - Gijs L. Kooij; Mike A. Botchev; Bernard J. Geurts (J. Comput. Appl. Math., 2017)

Exponential Krylov time integration for modeling multi-frequency optical response with monochromatic sources. - Mike A. Botchev; Abel M. Hanse; R. Uppu (J. Comput. Appl. Math., 2018)

An Exponential Time Integrator for the Incompressible Navier-Stokes Equation. - Gijs L. Kooij; Mike A. Botchev; Bernard J. Geurts (SIAM J. Sci. Comput., 2018)

Practical shift choice in the shift-and-invert Krylov subspace evaluations of the matrix exponential. - Alexandr Katrutsa; Mike A. Botchev; Ivan V. Oseledets (CoRR, 2019)

Predicting dynamical system evolution with residual neural networks. - Artem V. Chashchin; Mikhail A. Botchev; Ivan V. Oseledets; Grigory V. Ovchinnikov (CoRR, 2019)

An accurate restarting for shift-and-invert Krylov subspaces computing matrix exponential actions of nonsymmetric matrices. - Mikhail A. Botchev (CoRR, 2019)

A nested Schur complement solver with mesh-independent convergence for the time domain photonics modeling. - Mike A. Botchev (Comput. Math. Appl., 2020)

Exponential time integrators for unsteady advection-diffusion problems on refined meshes. - Mikhail A. Botchev (CoRR, 2020)

A residual concept for Krylov subspace evaluation of the 𝓁 matrix function. - Mike A. Botchev; Leonid A. Knizhnerman; Eugene E. Tyrtyshnikov (CoRR, 2020)

ART: Adaptive residual-time restarting for Krylov subspace matrix exponential evaluations. - Mikhail A. Botchev; Leonid A. Knizhnerman (J. Comput. Appl. Math., 2020)

Residual and Restarting in Krylov Subspace Evaluation of the φ Function. - Mike A. Botchev; Leonid Knizhnerman; Eugene E. Tyrtyshnikov (SIAM J. Sci. Comput., 2021)

Exponential Euler and backward Euler methods for nonlinear heat conduction problems. - Mikhail A. Botchev; Victor T. Zhukov (CoRR, 2022)

On convergence of waveform relaxation for nonlinear systems of ordinary differential equations. - Mike A. Botchev (CoRR, 2023)

Coarse Grid Corrections in Krylov Subspace Evaluations of the Matrix Exponential. - Mike A. Botchev (SIAM J. Sci. Comput., 2023)

Krylov Subspace Residual and Restarting for Certain Second Order Differential Equations. - Mike A. Botchev; Leonid Knizhnerman; Marcel Schweitzer (SIAM J. Sci. Comput., 2024)

Explicit adaptive time stepping for the Cahn-Hilliard equation by exponential Krylov subspace and Chebyshev polynomial methods. - Mike A. Botchev (CoRR, 2025)