Related papers: High Accuracy Method for Integral Equations with D…
The fractional Feynman-Kac equations describe the distribution of functionals of non-Brownian motion, or anomalous diffusion, including two types called the forward and backward fractional Feynman-Kac equations, where the fractional…
We present a novel approach for high-order accurate numerical differentiation on unstructured meshes of quadrilateral elements. To differentiate a given function, an auxiliary function with greater smoothness properties is defined which…
A symmetric characteristic singular integral equation with two fixed singularities at the endpoints in the class of functions bounded at the ends is analyzed. It reduces to a vector Hilbert problem for a half-disc and then to a vector…
Motivated by Fredholm theory, we develop a framework to establish the convergence of spectral methods for operator equations $\mathcal L u = f$. The framework posits the existence of a left-Fredholm regulator for $\mathcal L$ and the…
Finite difference schemes are the method of choice for solving nonlinear, degenerate elliptic PDEs, because the Barles-Sougandis convergence framework [Barles and Sougandidis, Asymptotic Analysis, 4(3):271-283, 1991] provides sufficient…
This study investigates the existence and uniqueness of solutions to Volterra integral equations with discontinuous kernels in both linear and nonlinear cases. The problem is two-dimensional, and the collocation method is employed to…
Direct numerical solution of the coordinate-space integral-equation version of the two-particle Lippmann Schwinger (LS) equation is considered as a means of avoiding the shortcomings of partial-wave expansion at high energies and in the…
This paper presents a universal numerical scheme tailored for tackling linear integral, integro-differential, and both initial and boundary value problems of ordinary differential equations. The numerical scheme is readily adapted for…
In this work, we study the numerical approximation of a class of singular fully coupled forward backward stochastic differential equations. These equations have a degenerate forward component and non-smooth terminal condition. They are…
We show that kernel-based quadrature rules for computing integrals can be seen as a special case of random feature expansions for positive definite kernels, for a particular decomposition that always exists for such kernels. We provide a…
In this paper, we investigate and analyze numerical solutions for the Volterra integrodifferential equations with tempered multi-term kernels. Firstly we derive some regularity estimates of the exact solution. Then a temporal-discrete…
We focus on a recently developed generalized pseudospectral method for accurate, efficient treatment of certain central potentials of interest in various branches in quantum mechanics, usually having singularity. Essentially this allows…
Stability and convergence of a time-weighted discrete scheme with nonuniform time steps are established for linear reaction-subdiffusion equations. The Caupto derivative is approximated at an offset point by using linear and quadratic…
The systems of nonlinear Volterra integral equations of the first kind with jump discontinuous kernels are studied. The iterative numerical method for such nonlinear systems is proposed. Proposed method employs the modified…
In this paper, we present Gauss's law-preserving spectral methods and their efficient solution algorithms for curl-curl source and eigenvalue problems in two and three dimensions arising from Maxwell's equations. Arbitrary order…
We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions. The selected methods lean on four different…
We introduce an integral representation of the Monge-Amp\`ere equation, which leads to a new finite difference method based upon numerical quadrature. The resulting scheme is monotone and fits immediately into existing convergence proofs…
A trigonometric interpolation algorithm for non-periodic functions has been recently proposed and applied to study general ordinary differential equation (ODE). This paper enhances the algorithm to approximate functions in $2$-dim space.…
In this article, we present an $O(N \log N)$ rapidly convergent algorithm for the numerical approximation of the convolution integral with radially symmetric weakly singular kernels and compactly supported densities. To achieve the reduced…
A novel high-order numerical scheme is proposed to compute the covariant derivative, particularly for divergence and curl, on any curved surface. The proposed scheme does not require the construction of a curved axis or metric tensor, which…