The Numerical Solution of the Heat Conduction Equation Subject to Separated Boundary Conditions | Zendy

M. R. Osborne | Zendy

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The Numerical Solution of the Heat Conduction Equation Subject to Separated Boundary Conditions

Author(s) -

M. R. Osborne

Publication year - 1969

Publication title -

the computer journal

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.319

H-Index - 64

eISSN - 1460-2067

pISSN - 0010-4620

DOI - 10.1093/comjnl/12.1.82

Subject(s) - mathematics , thermal conduction , heat equation , mathematical analysis , relativistic heat conduction , discretization , differential equation , boundary value problem , poincaré–steklov operator , partial differential equation , finite difference method , free boundary problem , thermodynamics , robin boundary condition , heat flux , physics , heat transfer

The stability of the Crank Nicolson scheme for the numerical solution of the heat conduction equation subject to separated boundary conditions is demonstrated. This result is extended to separable equations with variable coefficients and to the heat conduction equation in cylindrical geometry which has a singular coefficient. The solution of the difference approximation to the heat conduction equation is shown to reflect accurately the pattern of behaviour of the differential equation, and this result is applied to the phenomenon of 'persistent discretisation error' in the solution to the difference equation.

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