Related papers: Linearly Stabilized Schemes for the Time Integrati…

Time integration methods for solving initial value problems are an important component of many scientific and engineering simulations. Implicit time integrators are desirable for their stability properties, significantly relaxing…

We present a new strategy for solving stiff ODEs with explicit methods. By adaptively taking a small number of stabilizing small explicit time steps when necessary, a stiff ODE system can be stabilized enough to allow for time steps much…

In this note we propose and analyze novel implicit-explicit methods based on second order strong stability preserving multistep time discretizations. Several schemes are developed, and a linear stability analysis is performed to study their…

In this study, we propose high-order implicit and semi-implicit schemes for solving ordinary differential equations (ODEs) based on Taylor series expansion. These methods are designed to handle stiff and non-stiff components within a…

Stabilized explicit methods are particularly efficient for large systems of stiff stochastic differential equations (SDEs) due to their extended stability domain. However, they loose their efficiency when a severe stiffness is induced by…

A combination of implicit and explicit timestepping is analyzed for a system of ODEs motivated by ones arising from spatial discretizations of evolutionary partial differential equations. Loosely speaking, the method we consider is implicit…

Explicit stabilized methods are an efficient alternative to implicit schemes for the time integration of stiff systems of differential equations in large dimension. In this paper, we derive explicit stabilized integrators of orders one and…

For many systems of differential equations modeling problems in science and engineering, there are often natural splittings of the right hand side into two parts, one of which is non-stiff or mildly stiff, and the other part is stiff. Such…

We show that, even for extremely stiff systems, explicit integration may compete in both accuracy and speed with implicit methods if algebraic methods are used to stabilize the numerical integration. The required stabilizing algebra depends…

Fast and accurate solution of time-dependent partial differential equations (PDEs) is of key interest in many research fields including physics, engineering, and biology. Generally, implicit schemes are preferred over the explicit ones for…

Many interesting physical problems described by systems of hyperbolic conservation laws are stiff, and thus impose a very small time-step because of the restrictive CFL stability condition. In this case, one can exploit the superior…

Explicit stabilized integrators are an efficient alternative to implicit or semi-implicit methods to avoid the severe timestep restriction faced by standard explicit integrators applied to stiff diffusion problems. In this paper, we provide…

High-order discretizations of partial differential equations (PDEs) necessitate high-order time integration schemes capable of handling both stiff and nonstiff operators in an efficient manner. Implicit-explicit (IMEX) integration based on…

We present in this paper algorithms for solving stiff PDEs on the unit sphere with spectral accuracy in space and fourth-order accuracy in time. These are based on a variant of the double Fourier sphere method in coefficient space with…

The Immersed Boundary method has evolved into one of the most useful computational methods in studying fluid structure interaction. On the other hand, the Immersed Boundary method is also known to suffer from a severe timestep stability…

The use of implicit time-stepping schemes for the numerical approximation of solutions to stiff nonlinear time-evolution equations brings well-known advantages including, typically, better stability behaviour and corresponding support of…

An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…

Stochastic differential equations (SDE) often exhibit large random transitions. This property, which we denote as pathwise stiffness, causes transient bursts of stiffness which limit the allowed step size for common fixed time step explicit…

In this paper we address the question of whether it is possible to integrate time-dependent high-dimensional PDEs with hierarchical tensor methods and explicit time stepping schemes. To this end, we develop sufficient conditions for…

Forecasting physical signals in long time range is among the most challenging tasks in Partial Differential Equations (PDEs) research. To circumvent limitations of traditional solvers, many different Deep Learning methods have been…