1. New efficient numerical methods to describe the heat transfer in a solid medium
- Author
-
Sergio Blanes, Philipp Bader, and Enrique Ponsoda
- Subjects
Differential equation ,Differentiation (calculus) ,Computational costs ,Matrix boundary ,Integration ,Quasi-linearization ,Thermal energy ,Exponential integrator ,Exponential integrators ,Imbedding formulation ,Numerical integrations ,Boundary value problems ,Modelling and Simulation ,Efficient numerical method ,Numerical example ,Second orders ,Boundary value problem ,Second order exponential integrators ,Linear matrix ,Heat conduction ,Mathematics ,Boundary conditions ,Numerical analysis ,Mathematical analysis ,Thermal conduction ,Explicit method ,Solid medium ,Computer Science Applications ,Numerical integration ,Matrix boundary value problem ,Computational efficiency ,Modeling and Simulation ,Heat generation ,Heat transfer ,Numerical methods ,Nonlinear boundary value problems ,MATEMATICA APLICADA - Abstract
The analysis of heat conduction through a solid with heat generation leads to a linear matrix differential equation with separated boundary conditions. We present a symmetric second order exponential integrator for the numerical integration of this problem using the imbedding formulation. An algorithm to implement this explicit method in an efficient way with respect to the computational cost of the scheme is presented. This method can also be used for nonlinear boundary value problems if the quasilinearization technique is considered. Some numerical examples illustrate the performance of this method. © 2010 Elsevier Ltd., The authors acknowledge the support of the Generalitat Valenciana through the project GV/2009/032 and the Ministerio de Ciencia e Innovacion (Spain) under projects MTM2007-61572 and MTM2009-08587 (co-financed by the ERDF of the European Union).
- Published
- 2011