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Research Article Open access CC BY 4.0

Contribution to the Numerical Solution of Nonlinear Heat Transfer Equation Subject to a Boundary Integral Specification

Djibet Mbainguesse, Bakari Abbo, Youssouf Pare

Journal of Advances in Mathematics and Computer Science · pp. 48–57 · Published 3 Feb 2023

10.9734/jamcs/2023/v38i21745

Abstract

The work presents one dimensional heat transfer in a media with temperature-dependent thermal conductivity. We solve numerically the one-dimensional unsteady heat conduction equation subject to initial condition and integral boundary conditions. We first discertize the equation in time, using the implicite Euler time method. A sequence of nonlinear two-point boundary value problems is obtained. This discretisation reduce the problem to the second spatial derivative of temperature wich is a nonlinear function of the temperature and the temperature gradient. For the implementation of Newton method, we derive expressions for the partial derivative of the nonlinear function. Using higher order parallel splitting finite difference method and the Simpson's composite quadrature method, we solve the the resulting nonlinear systems by the multivariate Newton method. The MATLAB 2013a provides the approximate solution.

Nonlinear heat transfer boundary intagral specification implicit Euler method higher order paralell splitting finite difference method composite simpson quadrature newton method

References (7)

  1. 1 Solution of Equations and Systems of Equations [DOI]
  2. 2 Finite difference methods for a nonlocal boundary value problem for the heat equation [DOI]
  3. 3 Numerical solution of the heat equation with nonlocal boundary conditions [DOI]
  4. 4 Numerical solution of a parabolic equation with non-local boundary specifications [DOI]
  5. 5 Newton's Method in Banach Spaces [DOI]
  6. 6 Finite Difference Methods for Partial Differential Equations [DOI]
  7. 7 Higher order parallel splitting methods for parabolic partial differential equations

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