Linear regularized finite difference scheme for the quasilinear subdiffusion equation
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Alexander Lapin
und
Erkki Laitinen
Abstract
A homogeneous Dirichlet initial-boundary value problem for a quasilinear parabolic equation with a time-fractional derivative and coefficients at the elliptic part that depend on the gradient of the solution is considered. Conditions on the coefficients ensure the monotonicity and Lipschitz property of the elliptic operator on the set of functions whose gradients in space variables are uniformly bounded. For this problem, a linear regularized mesh scheme is constructed and investigated. A sufficient condition is derived for the regularization parameter that ensures the so-called local correctness of the mesh scheme. On the basis of correctness and approximation estimates for model problems with time-fractional Caputo or Caputo–Fabrizio derivatives, accuracy estimates are given in terms of mesh and regularization parameters under the assumption of the existence of a smooth solution to the differential problem. The presented results of the numerical experiments confirm the obtained asymptotic accuracy estimates.
Funding statement: This research was supported by Academy of Finland, grant No. 333448 (Alexander Lapin) and grant No. 333551 (Erkki Laitinen).
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© 2022 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Glacier parameterization in SLAV numerical weather prediction model
- Optimal disturbances for periodic solutions of time-delay differential equations
- Construction and optimization of numerically-statistical projection algorithms for solving integral equations
- Linear regularized finite difference scheme for the quasilinear subdiffusion equation
- On the efficiency of using correlative randomized algorithms for solving problems of gamma radiation transfer in stochastic medium
- Error identities for the reaction–convection–diffusion problem and applications to a posteriori error control
Artikel in diesem Heft
- Frontmatter
- Glacier parameterization in SLAV numerical weather prediction model
- Optimal disturbances for periodic solutions of time-delay differential equations
- Construction and optimization of numerically-statistical projection algorithms for solving integral equations
- Linear regularized finite difference scheme for the quasilinear subdiffusion equation
- On the efficiency of using correlative randomized algorithms for solving problems of gamma radiation transfer in stochastic medium
- Error identities for the reaction–convection–diffusion problem and applications to a posteriori error control
