References
- G. M. Amiraliyev, I. G. Amiraliyev, Mustafa Kudu,A numerical treatment for singularly perturbed differential equations with integral boundary condition, Applied mathematics and computation 185, 574-582,(2007). https://doi.org/10.1016/j.amc.2006.07.060
- D. Bahuguna, S.Abbas and J. Dabas, Partial functional differential equation with an integral condition and applications to population dynamics, Nonlinear Analysis 69 (2008) 2623-2635 https://doi.org/10.1016/j.na.2007.08.041
- D. Bahuguna and J. Dabas, Existence and Uniqueness of a Solution to a Semilinear Partial Delay Differential Equation with an Integral Condition, Nonlinear Dynamics and Systems Theory, 8 (1) (2008), 7-19.
- A. Boucherif, Second order boundary value problems with integral boundary condition, Nonlinear analysis, 70(1), 368-379, (2009).
- M. Cakir and G. M. Amiraliyev, A finite difference method for the singularly perturbed problem with nonlocal boundary condition, Applied mathematics and computation 160, 539-549,(2005). https://doi.org/10.1016/j.amc.2003.11.035
- J.R. Cannon , The solution of the heat equation subject to the specification of energy, Qart Appl Math 21(1963),155-160. https://doi.org/10.1090/qam/160437
- Y. S. Choi and Kwono-Yu Chan, A Parabolic equation with nonlocal boundary conditions arising from electrochemistry, Nonlinear Analysis Theory, Methods and Applications, Vol.18,No.4, pp.317-331,1992. https://doi.org/10.1016/0362-546X(92)90148-8
- W. A. Day, Parabolic equations and thermodynamics, Quart Appl Math 50(1992), 523-533. https://doi.org/10.1090/qam/1178432
- Hongyu Li and Fei Sun, Existence of solutions for integral boundary value prob- lems of second order ordinary differential equations, Li and Sun boundary value problems, (2012).
- M.K. Kadalbajoo, K.K. Sharma, Numerical treatment of boundary value problems for second order singularly perturbed delay differential equations, Comput. Appl. Math. 24(2), 151-172 (2005).
- M.K. Kadalbajoo,K.K. Sharma,Parameter-Uniform fitted mesh method for singularly perturbed delay differential equations with layer behavior. Electron. Trans. Numer. Anal. 23, 180-201 (2006).
- M.K. Kadalbajoo,D. Kumar, Fitted mesh B-spline collocation method for singularly perturbed differential equations with small delay, Appl. Math. Comput. 204, 90-98 (2008).
- C.G. Lange,R.M. Miura,Singularly perturbation analysis of boundary-value problems for differential-difference equations, SIAM J. Appl. Math. 42(3), 502-530 (1982). https://doi.org/10.1137/0142036
- Meigiang Feng, Dehong Ji, and Weigao Ge Positive solutions for a class of boundary value problem with integral boundary conditions in banach spaces, Journal of computational and applied mathematics 222, 351-363, (2008). https://doi.org/10.1016/j.cam.2007.11.003
- J.J.H. Miller,E. ORiordan,G.I. Shishkin, Fitted Numerical Methods for Singular Perturbation Problems,World Scientific Publishing Co., Singapore, New Jersey, London, Hong Kong (1996).
- Mustfa kudu and Gabil Amiraliyev, Finite difference method for a singularly perturbed differential equations with integral boundary condition, International journal of mathematics and computation Vol (26),(2015).
- S.Nicaise, C.Xenophontos, Robust approximation of singularly perturbed delay differential equations by the hp finite element method. Comput. Meth. Appl. Math. 13(1), 21-37 (2013).
- Z.Q. Tang, F.Z. Geng, Fitted reproducing kernel method for singularly perturbed delay initial value problems, Applied Mathematics and Computation 284 (2016) 169-174. https://doi.org/10.1016/j.amc.2016.03.006
- H. Zarin, On discontinuous Galerkin finite element method for singularly perturbed delay differential equations, Applied Mathematics Letters 38 (2014) 27-32. https://doi.org/10.1016/j.aml.2014.06.013
- Zhang Lian and Xie Feng, Singularly perturbed first order differential equations with integral boundary condition, J. Shanghai Univ (Eng), 20-22, (2009).
- Zhongdi Cen and Xin Cai, A second order upwind difference scheme for a sin- gularly perturbed problem with integral boundary condition in netural network , Springer verlag berlin heidelberg, 175-181, 2007.
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