A parabolic equation with nonlocal boundary conditions arising from electrochemistry
Nonlinear Analysis: Theory, Methods & Applications
General nonlocal nonlinear boundary value problem for differential equation of 3rd order
Nonlinear Analysis: Theory, Methods & Applications
On a nonlocal elliptic problem arising in the magnetic confinement of a plasma in a Stellarator
Proceedings of second world congress on Nonlinear analysts
SIAM Journal on Numerical Analysis
Efficient techniques for the second-order parabolic equation subject to nonlocal specifications
Applied Numerical Mathematics
Finite Differences And Partial Differential Equations
Finite Differences And Partial Differential Equations
On the stability of exponential fitting BDF algorithms
Journal of Computational and Applied Mathematics - Special issue: Selected papers of the international conference on computational methods in sciences and engineering (ICCMSE-2003)
Exponential fitting BDF algorithms: explicit and implicit 0-stable methods
Journal of Computational and Applied Mathematics - Special issue on computational and mathematical methods in science and engineering (CMMSE-2004)
Adapted BDF Algorithms: Higher-order Methods and Their Stability
Journal of Scientific Computing
Explicit finite difference schemes adapted to advection-reaction equations
International Journal of Computer Mathematics - Recent Advances in Computational and Applied Mathematics in Science and Engineering
Applied Numerical Mathematics
Finite difference method for multipoint nonlocal elliptic-parabolic problems
Computers & Mathematics with Applications
Computers & Mathematics with Applications
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Many physical phenomena are modelled by nonclassical parabolic boundary value problems with nonlocal boundary conditions. Many different papers studied the second-order parabolic equation, particularly the heat equation subject to the specifications of mass. In this paper, we provide a whole family of new algorithms that improve the CPU time and accuracy of Crandall's formula shown in [J. Martin-Vaquero, J. Vigo-Aguiar, A note on efficient techniques for the second-order parabolic equation subject to non-local conditions, Appl. Numer. Math. 59 (6) (2009) 1258-1264] (and this algorithm improved the results obtained with BTCS, FTCS or Dufort-Frankel three-level techniques previously used in other works, see [M. Dehghan, Efficient techniques for the second-order parabolic equation subject to nonlocal specifications, Appl. Numer. Math. 52 (2005) 39-62]) with this kind of problems. Other methods got second or fourth order only when k=sh^2, while the new codes got nth order for k=h; therefore, the new schemes require a smaller storage and CPU time employed than other algorithms. We will study the convergence of the new algorithms and finally we will compare the efficiency of the new methods with some well-known numerical examples.