The application of the local polynomial and non-polynomial to the construction of methods for numerically solving the heat conduction problem is discussed. The non-polynomial splines are used here to approximate the partial derivatives. Formulas for numerical differentiation based on the application of the non-polynomial splines of the fourth order of approximation are constructed. Particular attention is paid to polynomial, trigonometric, exponential, polynomial-trigonometric and polynomial-exponential splines. This approach allows us to construct explicit and implicit difference schemes. The main focus of the paper is on implicit difference scheme. New approximations with splines of the Lagrange and Hermite type with new properties are obtained. These approximations take into account the first and second derivatives of the function being approximated. Numerical examples are given.

Original languageEnglish
Pages (from-to)531-548
Number of pages18
JournalWSEAS Transactions on Mathematics
Volume19
DOIs
StatePublished - 2 Nov 2020

    Research areas

  • Exponential splines, Heat conduction problem, Polynomial splines, Polynomial-exponential splines, Polynomial-trigonometric splines, Trigonometric splines

    Scopus subject areas

  • Algebra and Number Theory
  • Endocrinology, Diabetes and Metabolism
  • Statistics and Probability
  • Discrete Mathematics and Combinatorics
  • Management Science and Operations Research
  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

ID: 72515508