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Staggered grid finite difference scheme is widely used for the first order elastic wave equation, which constitutes the basis for least-squares reverse time migration and full waveform inversion. It is of great importance to improve the…
In this work, we develop a localized numerical scheme with low regularity requirements for solving time-fractional integro-differential equations. First, a fully discrete numerical scheme is constructed. Specifically, for temporal…
In this work, we present a new high order Discontinuous Galerkin time integration scheme for second-order (in time) differential systems that typically arise from the space discretization of the elastodynamics equation. By rewriting the…
We present an adaptation of the so-called structural method \cite{CMM23} for Hamiltonian systems, and redesign the method for this specific context, which involves two coupled differential systems. Structural schemes decompose the problem…
This paper provides a finite difference discretization for the backward Feynman-Kac equation, governing the distribution of functionals of the path for a particle undergoing both reaction and diffusion [Hou and Deng, J. Phys. A: Math.…
Invariant discretization schemes are derived for the one- and two-dimensional shallow-water equations with periodic boundary conditions. While originally designed for constructing invariant finite difference schemes, we extend the usage of…
A method for constructing first integral preserving numerical schemes for time-dependent partial differential equations on non-uniform grids is presented. The method can be used with both finite difference and partition of unity approaches,…
We consider difference schemes for nonlinear time fractional Klein-Gordon type equations in this paper. A linearized scheme is proposed to solve the problem. As a result, iterative method need not be employed. One of the main difficulties…
This paper presents a new approach and methodology to solve the second order one dimensional hyperbolic telegraph equation with Dirichlet and Neumann boundary conditions using the cubic trigonometric B-spline collocation method. The usual…
Space fractional convection diffusion equation describes physical phenomena where particles or energy (or other physical quantities) are transferred inside a physical system due to two processes: convection and superdiffusion. In this…
In this paper, we design, analyze, and numerically validate positive and energy-dissipating schemes for solving the time-dependent multi-dimensional system of Poisson-Nernst-Planck (PNP) equations, which has found much use in the modeling…
In this paper, we propose and analyze a second-order time-stepping numerical scheme for the inhomogeneous backward fractional Feynman-Kac equation with nonsmooth initial data. The complex parameters and time-space coupled Riemann-Liouville…
In this paper, a linearized fully discrete scheme is proposed to solve the two-dimensional nonlinear time fractional Schr\"odinger equation with weakly singular solutions, which is constructed by using L1 scheme for Caputo fractional…
A time-fractional Allen-Cahn equation with volume constraint is first proposed by introducing a nonlocal time-dependent Lagrange multiplier. Adaptive linear second-order energy stable schemes are developed for the proposed model by…
We consider a control constrained parabolic optimal control problem and use variational discretization for its time semi-discretization. The state equation is treated with a Petrov-Galerkin scheme using a piecewise constant Ansatz for the…
The numerical solution of a nonlinear and space-fractional anti-diffusive equation used to model dune morphodynamics is considered. Spatial discretization is effected using a finite element method whereas the Crank-Nicolson scheme is used…
In this paper, we introduce and analyze a class of numerical schemes that demonstrate remarkable superiority in terms of efficiency, the preservation of positivity, energy stability, and high-order precision to solve the time-dependent…
A well-balanced second order finite volume central scheme for the magnetohydrodynamic (MHD) equations with gravitational source term is developed in this paper. The scheme is an unstaggered central scheme that evolves the numerical solution…
In this paper, an alternating direction implicit (ADI) difference scheme for two-dimensional time-fractional wave equation of distributed-order with a nonlinear source term is presented. The unique solvability of the difference solution is…
In this article we discuss the numerical analysis for the finite difference scheme of the one-dimensional nonlinear wave equations with dynamic boundary conditions. From the viewpoint of the discrete variational derivative method we propose…