In this paper, a novel method presented in [1] is applied to solve time-fractional Kudryashov-
Sinelshchikov equation (KS equation), a nonlinear fractional partial differential equation …

Through the utilized investigation, a novel algorithm in reproducing kernel Hilbert approach
is applied to generate pointwise numerical solution to time-fractional Burgers' model in …

This article aims to achieve robust numerical results by applying the Chebyshev reproducing
kernel method without homogenizing the initial‐boundary conditions of the Emden–Fowler …

Mathematical models have been frequently studied in recent decades in order to obtain the
deeper properties of real-world problems. In particular, if these problems, such as finance …

In this paper, we give an investigation on the problem of solving Laplace equation with the
kernel regularized regression. We provide a Sobolev type space corresponding to the …

In this article, a new reproducing kernel approach is developed for obtaining a numerical
solution of multi-order fractional nonlinear three-point boundary value problems. This …

In this study, an effective approach is presented to obtain a numerical solution of linear and
nonlinear singular boundary value problems. The proposed method is constructed by …

In this research, the Lax, the Upwind, and the MacCormack finite difference methods are
applied to the experimental solving of the one-dimensional (1D) unsteady Burger's …

Bu tez yedi bölümden oluşmaktadır. Birinci bölümde, kesir mertebeli türev ve doğuran
çekirdekli Hilbert uzayı metodu hakkında tarihsel gelişim ve literatür taraması verilmiştir …

The intention of this thesis is to evaluate the high-performance machine learning framework
JAX. In the course of this work, a physics-informed neural network that solves the Burgers' …