A Galerkin procedure for the diffusion equation subject to the specification of mass
SIAM Journal on Numerical Analysis
Finite difference schemes and partial differential equations
Finite difference schemes and partial differential equations
Applied Numerical Mathematics
The reformulation and numerical solution of certain nonclassical initial-boundary value problems
SIAM Journal on Scientific and Statistical Computing
Solving parabolic integro-differential equations by an explicit integration method
Journal of Computational and Applied Mathematics
A parabolic equation with nonlocal boundary conditions arising from electrochemistry
Nonlinear Analysis: Theory, Methods & Applications
Weak solution to an evolution problem with a nonlocal constraint
SIAM Journal on Mathematical Analysis
Product integration methods for solving a system of nonlinear Volterra integral equations
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Numerical solution of the heat equation with nonlocal boundary conditions
Journal of Computational and Applied Mathematics
ACM Transactions on Mathematical Software (TOMS)
Computers & Mathematics with Applications
Computers & Mathematics with Applications
On a parabolic inclusion with integral boundary conditions
MATH'08 Proceedings of the American Conference on Applied Mathematics
Determination of a time-dependent heat transfer coefficient from non-standard boundary measurements
Mathematics and Computers in Simulation
Applied Numerical Mathematics
Numerical algorithm for parabolic problems with non-classical conditions
Journal of Computational and Applied Mathematics
On the numerical solution of the heat conduction equations subject to nonlocal conditions
Applied Numerical Mathematics
Direct numerical method for an inverse problem of a parabolic partial differential equation
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Parallel LOD scheme for 3d parabolic problem with nonlocal boundary condition
Euro-Par'06 Proceedings of the 12th international conference on Parallel Processing
Mathematical and Computer Modelling: An International Journal
Mathematical and Computer Modelling: An International Journal
The Chebyshev spectral viscosity method for the time dependent Eikonal equation
Mathematical and Computer Modelling: An International Journal
Mathematical and Computer Modelling: An International Journal
Parameter determination in a partial differential equation from the overspecified data
Mathematical and Computer Modelling: An International Journal
Computers & Mathematics with Applications
Solving a parabolic PDE with nonlocal boundary conditions using the Sinc method
Numerical Algorithms
Applied Numerical Mathematics
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Many physical phenomena are modeled by nonclassical parabolic boundary value problems with nonlocal boundary conditions. In place of the classical specification of boundary data, we impose a nonlocal boundary condition. Partial differential equations with nonlocal boundary conditions have received much attention in the last twenty years. Most of the papers were directed to the second-order parabolic equation, particularly to the heat conduction equation. One could generically classify these problems into two types; boundary value problems with nonlocal initial conditions, and boundary value problems with nonlocal boundary conditions. We will deal here with the second type of nonlocal boundary value problems that is the solution of nonlocal boundary value problems with standard initial condition. The main difficulty in the implicit treatment of the nonlocal boundary value problems is the nonclassical form of the resulting matrix of the system of linear algebraic equations. In this paper, various approaches for the numerical solution of the one-dimensional heat equation subject to the specification of mass which have been considered in the literature, are reported. Several methods have been proposed for the numerical solution of this boundary value problem. Some remarks comparing our work with earlier work will be given throughout the paper. Numerical examples are given at the end of this paper to compare the efficiency of the new techniques. Some specific applications in engineering models are introduced.