Related papers: Generalized extrapolation methods based on composi…
A new family of methods involving complex coefficients for the numerical integration of differential equations is presented and analyzed. They are constructed as linear combinations of symmetric-conjugate compositions obtained from a basic…
This paper presents a class of Two-Step General Linear Methods for the numerical solution of Retarded Functional Differential Equations. Explicit methods up to order five are constructed. To avoid order reduction for mildly stiff problems…
This paper presents a class of Two-Step General Linear Methods for the numerical solution of Retarded Functional Differential Equations. Explicit methods up to order five are constructed. To avoid order reduction for mildly stiff problems…
Splitting methods for the numerical integration of differential equations of order greater than two involve necessarily negative coefficients. This order barrier can be overcome by considering complex coefficients with positive real part.…
We show that a generalised sparse grid combination technique which combines multi-variate extrapolation of finite difference solutions with the standard combination formula lifts a second order accurate scheme on regular meshes to a fourth…
This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…
We analyze composition methods with complex coefficients exhibiting the so-called ``symmetry-conjugate'' pattern in their distribution. In particular, we study their behavior with respect to preservation of qualitative properties when…
The total generalized variation extends the total variation by incorporating higher-order smoothness. Thus, it can also suffer from similar discretization issues related to isotropy. Inspired by the success of novel discretization schemes…
Recently Ahmadi et al. (2021) and Tagliaferro (2022) proposed some iterative methods for the numerical solution of linear systems which, under the classical hypothesis of strict diagonal dominance, typically converge faster than the Jacobi…
New families of composition methods with processing of order 4 and 6 are presented and analyzed. They are specifically designed to be used for the numerical integration of differential equations whose vector field is separated into three or…
New families of fourth-order composition methods for the numerical integration of initial value problems defined by ordinary differential equations are proposed. They are designed when the problem can be separated into three parts in such a…
The new class of alternating-conjugate splitting methods is presented and analyzed. They are obtained by concatenating a given composition involving complex coefficients with the same composition but with the complex conjugate coefficients.…
High order methods are often desired for the evolution of ordinary differential equations, in particular those arising from the semi-discretization of partial differential equations. In prior work in we investigated the interplay between…
The recently introduced polynomial time integration framework proposes a novel way to construct time integrators for solving systems of first-order ordinary differential equation by using interpolating polynomials in the complex time plane.…
This work proposes a methodology to develop new numerical integration algorithms for ordinary differential equations based on state quantization, generalizing the notions of Linearly Implicit Quantized State Systems (LIQSS) methods. Using…
The generalized-$\alpha$ method encompasses a wide range of time integrators. The method possesses high-frequency dissipation while minimizing unwanted low-frequency dissipation and the numerical dissipation can be controlled by the user.…
Lie's linearizability criteria for scalar second-order ordinary differential equations had been extended to systems of second-order ordinary differential equations by using geometric methods. These methods not only yield the linearizing…
Numerically solving ordinary differential equations (ODEs) is a naturally serial process and as a result the vast majority of ODE solver software are serial. In this manuscript we developed a set of parallelized ODE solvers using…
In [7], a new iterative method for solving linear system of equations was presented which can be considered as a modification of the Gauss-Seidel method. Then in [4] a different approach, say 2D-DSPM, and more effective one was introduced.…
The method of this paper is my original creation. A new method for solving linear differential equations is proposed in this paper. The important conclusion of this paper is that arbitrary order linear ordinary differential equations with…