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KIAM Preprint № 69, Moscow, 2023
Authors: Botchev M.A., Zhukov V.T.
Exponential Euler and backward Euler methods for nonlinear heat conduction problems
In this paper a variant of nonlinear exponential Euler scheme is proposed for solving nonlinear heat conduction problems. The method is based on nonlinear iterations where at each iteration a linear initial-value problem has to be solved. We compare this method to the backward Euler method combined with nonlinear iterations. For both methods we show monotonicity and boundedness of the solutions and give sufficient conditions for convergence of the nonlinear iterations. Numerical tests are presented to examine performance of the two schemes. The presented exponential Euler scheme is implemented based on restarted Krylov subspace methods and, hence, is essentially explicit (involves only matrix-vector products).
nonlinear heat conduction, exponential time integration, matrix exponential, Krylov subspace methods
Publication language: russian,  pages: 16
Research direction:
Theoretical and applied problems of mechanics
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About authors:
  • Botchev Mikhail Aleksandrovich, RAS
  • Zhukov Victor Timofeevich, RAS