Matrix analysis
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
A stability result for sectorial operators in branch spaces
SIAM Journal on Numerical Analysis
Stability of rational multistep approximations of holomorphic semigroups
Mathematics of Computation
Applied Numerical Mathematics
Numerical solution of the heat equation with nonlocal boundary conditions
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
A numerical approach for a semilinear parabolic equation with a nonlocal boundary condition
Journal of Computational and Applied Mathematics
A nonlinear parabolic equation with a nonlocal boundary term
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
Solving a parabolic PDE with nonlocal boundary conditions using the Sinc method
Numerical Algorithms
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This paper deals with numerical methods for the solution of the heat equation with integral boundary conditions. Finite differences are used for the discretization in space. The matrices specifying the resulting semidiscrete problem are proved to satisfy a sectorial resolvent condition, uniformly with respect to the discretization parameter.Using this resolvent condition, unconditional stability is proved for the fully discrete numerical process generated by applying A(θ)-stable one-step methods to the semidiscrete problem. This stability result is established in the maximum norm; it improves some previous results in the literature in that it is not subject to various unnatural restrictions which were imposed on the boundary conditions and on the one-step methods.