In this paper we consider a class of singular two-point boundary value problem: (xαu')' = f(x, u), u(0) = A, u(1) = B, 0 < α < 1. The asymptotic expression of the spline finite difference solution for ...

11: Finite difference methods for boundary value problems. The shooting method replaces the given BVP with a family of IVPs which it solves numerically until it finds one that closely approximates the ...

1.3 Introduction to functional analysis PDF html md 2 Elliptic problems 2.1 Elliptic problems PDF html md 2.2 Finite differences for elliptic problems PDF html md 2.3 Finite elements for elliptic ...

A new approach in the finite difference framework is developed, which consists of three steps: choosing the dimension of the local approximation subspace, constructing a vector basis for this subspace ...

ABSTRACT: The solution of the Riemann Problem (RP) for the one-dimensional (1D) non-linear Shallow Water Equations (SWEs) is known to produce four potential wave patterns for the scenario where the ...

ABSTRACT: This paper presents a comprehensive numerical study of the two-dimensional time-dependent heat conduction equation using the Forward Time Centered Space (FTCS) finite difference scheme. The ...

Finite element methods (FEM) have become indispensable tools for simulating wave propagation phenomena across a range of applications, from acoustics and electromagnetics to earthquake modelling. At ...