Related papers: Dimensional splitting of hyperbolic partial differ…
The supersymmetrical intertwining relations are the most productive part of the supersymmetrical method in two-dimensional Quantum Mechanics. Most interesting are relations with hyperbolic form of derivatives in supercharges. So far,…
In recent years, tremendous progress has been made on numerical algorithms for solving partial differential equations (PDEs) in a very high dimension, using ideas from either nonlinear (multilevel) Monte Carlo or deep learning. They are…
The time-dependent fields obtained by solving partial differential equations in two and more dimensions quickly overwhelm the analytical capabilities of the human brain. A meaningful insight into the temporal behaviour can be obtained by…
The hyperbolic Radon transform is a commonly used tool in seismic processing, for instance in seismic velocity analysis, data interpolation and for multiple removal. A direct implementation by summation of traces with different moveouts is…
Mixed-dimensional partial differential equations arise in several physical applications, wherein parts of the domain have extreme aspect ratios. In this case, it is often appealing to model these features as lower-dimensional manifolds…
Motivated by important applications in image processing, we study a class of second-order geometric quasilinear hyperbolic partial differential equations (PDEs). This is inspired by the recent development of second-order damping systems…
In this paper we develop a dressing method for constructing and solving some classes of matrix quasi-linear Partial Differential Equations (PDEs) in arbitrary dimensions. This method is based on a homogeneous integral equation with a…
We present domain decomposition finite element/finite difference method for the solution of hyperbolic equation. The domain decomposition is performed such that finite elements and finite differences are used in different subdomains of the…
We represent an algorithm allowing one to construct new classes of partially integrable multidimensional nonlinear partial differential equations (PDEs) starting with the special type of solutions to the (1+1)-dimensional hierarchy of…
The differential transform method (DTM) is a relatively new technique that may be used to find a series solution to differential equations (both linear and nonlinear) through an iterative process. This brief manuscript is an initial effort…
This article describes a numerical method based on the dual reciprocity boundary elements method (DRBEM) for solving some well-known nonlinear parabolic partial differential equations (PDEs). The equations include the classic and…
Spectral methods for solving partial differential equations (PDEs) and stochastic partial differential equations (SPDEs) often use Fourier or polynomial spectral expansions on either uniform and non-uniform grids. However, while very widely…
This paper extends backstepping to higher-dimensional PDEs by leveraging domain symmetries and structural properties. We systematically address three increasingly complex scenarios. First, for rectangular domains, we characterize boundary…
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…
In this paper, we present a splitting algorithm to solve multicomponent transport models. These models are related to plasma simulations, in which we consider the local thermodynamic equilibrium and weakly ionised plasma-mixture models that…
We develop an unsupervised machine learning algorithm for the automated discovery and identification of traveling waves in spatio-temporal systems governed by partial differential equations (PDEs). Our method uses sparse regression and…
We propose a variational splitting technique for the generalized-$\alpha$ method to solve hyperbolic partial differential equations. We use tensor-product meshes to develop the splitting method, which has a computational cost that grows…
In this article, we develop a systematic approach of the invariant subspace method combined with variable transformation to find the generalized separable exact solutions of the nonlinear two-component system of time-fractional PDEs…
Recent years have witnessed a growth in mathematics for deep learning--which seeks a deeper understanding of the concepts of deep learning with mathematics and explores how to make it more robust--and deep learning for mathematics, where…
A second-order $L$-stable exponential time-differencing (ETD) method is developed by combining an ETD scheme with approximating the matrix exponentials by rational functions having real distinct poles (RDP), together with a dimensional…