The use of Adomian decomposition method for solving the one-dimensional parabolic equation with non-local boundary specifications

References

• Adomian G. (1994) Solving Frontier Problems of Physics: The Decomposition Method Kluwer Boston
   Google Scholar
• Adomian , G. (1988) . A review of the decomposition method in applied mathematics . J. Math. Anal. Appl. , 135 : 501 – 544 .
   Web of Science ®Google Scholar
• Adomian , G. (1987) . Modification of the decomposition approach to the heat equation . J. Math. Anal. Appl. , 124 : 290 – 291 .
   Web of Science ®Google Scholar
• Adomian , G. (1986) . A new approach to the heat equation, an application of the decomposition method . J. Math. Anal. Appl. , 113 : 202 – 209 .
   Web of Science ®Google Scholar
• Adomian , G. (1991) . Solving frontier problems modelled by nonlinear partial differential equtions . Comput. Math. Appl. , 22 : 91 – 94 .
   Web of Science ®Google Scholar
• Ang , W. T. (2002) . A method of solution for the one-dimensional heat equation subject to a nonlocal condition . SEA Bulletin of Mathematics , 26 ( 2 ) : 197 – 203 .
   Google Scholar
• Cannon , J. R. , Lin , Y. and Wang , S. (1990) . An implicit finite difference scheme for the diffusion equation subject to mass specification . Internat. J. Engng. Sci. , 28 ( 7 ) : 573 – 578 .
   Web of Science ®Google Scholar
• Cannon , J. R. and van der Hoek , J. (1986) . Diffusion subject to specification of mass . J. Math. Anal. Appl. , 115 : 517 – 529 .
   Web of Science ®Google Scholar
• Cannon , J. R. , Esteva , S. P. and van der Hoek , J. (1987) . A Galerkin procedure for the diffusion equation subject to the specification of mass . SIAM J. Numer. Anal. , 24 : 499 – 515 .
   Web of Science ®Google Scholar
• Cannon , J. R. and Yin , H. M. (1989) . On a class of non-classical parabolic problems . J. Differential Equations , 79 : 266 – 288 .
   Web of Science ®Google Scholar
• Capasso , V. and Kunisch , K. (1988) . A reaction-diffusion system arising in modeling man-environment diseases . Quart. Appl. Math. , 46 : 431 – 449 .
   Web of Science ®Google Scholar
• Cherruault , Y. (1990) . Convergence of Adomian's method . Math. Comput. Modelling , 14 : 83 – 86 .
   Google Scholar
• Datta , B. K. (1989) . A new approach to the wave equation – An application of the decomposition method . J. Math. Anal. Appl. , 142 : 6 – 12 .
   Web of Science ®Google Scholar
• Day , W. A. (1982) . Existence of a property of solutions of the heat equation subject to linear thermoelasticity and other theories . Quart. Appl. Math. , 40 : 319 – 330 .
   Web of Science ®Google Scholar
• Day , W. A. (1983) . A decreasing property of solutions of a parabolic equation with applications to thermoelasticity and other theories . Quart. Appl. Math. , 41 : 468 – 475 .
   Web of Science ®Google Scholar
• Dehghan M. Numerical solution of a parabolic equation with non-local boundary specifications Applied Mathematics and Computation in press
   Google Scholar
• Ekolin , G. (1991) . Finite difference methods for a non-local boundary value problem for the heat equation . BIT , 31 ( 2 ) : 245 – 255 .
   Web of Science ®Google Scholar
• Friedman , A. (1986) . Monotonic decay of solutions of parabolic equation with nonlocal boundary conditions . Quart. Appl. Math. , 44 : 468 – 475 .
   Web of Science ®Google Scholar
• Kawohl , B. (1987) . Remark on a paper by D. A. Day on a maximum principle under nonlocal boundary conditions . Quart. Appl. Math. , 45 : 751 – 752 .
   Web of Science ®Google Scholar
• Kaya , D. (2000) . An application of the decomposition method to he second-order wave equation . Internat. J. Comput. Math. , 75 : 235 – 245 .
   Web of Science ®Google Scholar
• Lesnic , D. (2001) . A computational algebraic investigation of the decomposition method for time-dependent problems . Appl. Math. Comput. , 119 : 197 – 206 .
   Web of Science ®Google Scholar
• Lin , Y. , Xu , S. and Yin , H. M. (1997) . Finite difference approximations for a class of nonlocal parabolic equations . Intern. J. Math. and Math. Sci. , 20 ( 1 ) : 147 – 164 .
   Google Scholar
• Liu , Y. (1999) . Numerical solution of the heat equation with nonlocal boundary conditions . J. Comput. Appl. Math. , 110 ( 1 ) : 115 – 127 .
   Web of Science ®Google Scholar
• Wang , S. and Lin , Y. (1990) . A numerical method for the diffusion equation with nonlocal boundary specifications . Intern. J. Engng. Sci. , 28 : 543 – 546 .
   Web of Science ®Google Scholar
• Wang , S. and Lin , Y. (1989) . A finite difference solutions to an inverse problem determining a control function in a parabolic partial differential equations . Inverse Problems , 5 : 631 – 640 .
   Web of Science ®Google Scholar
• Wazwaz , A. M. (1999) . A reliable modification of Adomian decomposition method . Appl. Math. Comput. , 102 : 77 – 86 .
   Web of Science ®Google Scholar
• Yee , E. (1993) . Application of the decomposition method to the solution of the reaction-convection-diffusion equation . Appl. Math. Comput. , 56 : 1 – 27 .
   Web of Science ®Google Scholar