Related papers: Reproducing kernel method for PDE constrained opti…
In this paper we investigate and compare different gradient algorithms designed for the domain expression of the shape derivative. Our main focus is to examine the usefulness of kernel reproducing Hilbert spaces for PDE constrained shape…
In this paper we combine the theory of reproducing kernel Hilbert spaces with the field of collocation methods to solve boundary value problems with special emphasis on reproducing property of kernels. From the reproducing property of…
This article is concerned with an approximate analytical solution for the time fractional Kudryashov Sinelshchikov equation by using the reproducing kernel Hilbert space method. The main tools of this method are reproducing kernel theory,…
In this article, the reproducing kernel Hilbert space [0, 1] is employed for solving a class of third-order periodic boundary value problem by using fitted reproducing kernel algorithm. The reproducing kernel function is built to get fast…
In this paper, we discuss the solution of certain matrix-valued partial differential equations. Such PDEs arise, for example, when constructing a Riemannian contraction metric for a dynamical system given by an autonomous ODE. We develop…
In this paper, we present a fast and accurate numerical scheme for the solution of fifth-order boundary-value problems. We apply the reproducing kernel Hilbert space method (RKHSM) for solving this problem. The analytic results of the…
Much recent work has addressed the solution of a family of partial differential equations by computing the inverse operator map between the input and solution space. Toward this end, we incorporate function-valued reproducing kernel Hilbert…
We develop a kernel-based solver for path-dependent PDEs (PPDEs) along with a convergence theory. Our numerical scheme leverages signature kernels, a recently introduced class of kernels on path-space. Specifically, we solve an optimal…
This article is concerned with solving the time fractional Vakhnenko Parkes equation using the reproducing kernels. Reproducing kernel theory, the normal basis, some important Hilbert spaces, homogenization of constraints, and the…
We present a method to construct a chain of reproducing kernel Hilbert spaces controlled by a first-order system of differential equations from a given unimodular function satisfying several conditions. One of the applications of that…
In this research, a new numerical method is proposed for solving fractional Bratu type boundary value problems. Fractional derivatives are taken in Caputo sense. This method is predicated on iterative approach of reproducing kernel Hilbert…
The aim of this study is to present a good modernistic strategy for solving some well-known classes of Lane-Emden type singular differential equations. The proposed approach is based on the reproducing kernel Hilbert space (RKHS) and…
The numerical solution methods for partial differential equation (PDE) solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods…
In this paper, we present an iterative reproducing kernel method for numerical solution of one dimensional fractional Burgers equation with variable coefficient. Convergence analysis is constructed theoretically. Numerical experiments show…
In this paper we present the theoretical framework needed to justify the use of a kernel-based collocation method (meshfree approximation method) to estimate the solution of high-dimensional stochastic partial differential equations…
We propose a kernel compression method for solving Distributed-Order (DO) Fractional Partial Differential Equations (DOFPDEs) at the cost of solving corresponding local-in-time PDEs. The key concepts are (1) discretization of the integral…
We characterize the reproducing kernel Hilbert spaces whose elements are $p$-integrable functions in terms of the boundedness of the integral operator whose kernel is the reproducing kernel. Moreover, for $p=2$ we show that the spectral…
Reduced modeling in high-dimensional reproducing kernel Hilbert spaces offers the opportunity to approximate efficiently non-linear dynamics. In this work, we devise an algorithm based on low rank constraint optimization and kernel-based…
We study kernel functions, and associated reproducing kernel Hilbert spaces $\mathscr{H}$ over infinite, discrete and countable sets $V$. Numerical analysis builds discrete models (e.g., finite element) for the purpose of finding…
This paper is concerned with the numerical minimization of energy functionals in Hilbert spaces involving convex constraints coinciding with a semi-norm for a subspace. The optimization is realized by alternating minimizations of the…