Journal Article10.1007/BF01931285
Finite difference methods for a nonlocal boundary value problem for the heat equation
110
TL;DR: In this paper, three different finite difference schemes for solving the heat equation in one space dimension with boundary conditions containing integrals over the interior of the interval are considered, based on the forward Euler, the backward Euler and the Crank-Nicolson methods.
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Abstract: Three different finite difference schemes for solving the heat equation in one space dimension with boundary conditions containing integrals over the interior of the interval are considered. The schemes are based on the forward Euler, the backward Euler and the Crank-Nicolson methods. Error estimates are derived in maximum norm. Results from a numerical experiment are presented.
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Numerical Solutions of Partial Differential Equations
Silvia Bertoluzza,Silvia Falletta,Giovanni Russo,Chi-Wang Shu +3 more
- 10 Dec 2008
TL;DR: This presentation explains the development of the Discontinuous Galerkin Method for PDEs Containing Higher-Order Spatial Derivatives and its applications in conservation laws and systems with Stiff Source.
181
Monotonic decay of solutions of parabolic equations with nonlocal boundary conditions
TL;DR: Soit A≡Σ i,j=1 u a ij (x)∂ 2 /∂x i ∂x j + Σ i = 1 u bi(x) ∂ 2 ∂ x ∂ j + ∂ X ∈ C(Ω) as discussed by the authors.
Remarks on a paper by W. A. Day on a maximum principle under nonlocal boundary conditions
TL;DR: In this article, the authors extend the decay property for solutions to a linear parabolic equation with nonlocal boundary conditions to arbitrary space dimensions, and from linear to nonlinear parabolic equations and from differential equations to differential inequalities.