Applications of Radial Basis Functions: Sobolev-Orthogonal Functions, Radial Basis Functions and Spectral Methods

Abstract

In this paper we consider an application of Sobolev-orthogonal functions and radial basis function to the numerical solution of partial differential equations. We develop the fundamentals of a spectral method, present examples via reaction-diffusion partial differential equations and discuss briefly some links with theory of wavelets.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 2001
Accession Number
ADP013730

Entities

People

  • A. Iserles
  • M. D. Buhmann
  • S. P. Norsett

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Bessel Functions
  • Coefficients
  • Computations
  • Differential Equations
  • Diffusion
  • Diffusion Coefficient
  • Equations
  • Infinite Series
  • Integrals
  • Linear Systems
  • Nonlinear Systems
  • Orthogonality
  • Partial Differential Equations
  • Polynomials
  • Quadratic Equations
  • Technical Information Centers
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)