### Solution of a Class of Fourth Order Singular Singularly Perturbed Boundary Value Problems by Haar Wavelets Method and Quintic B-Spline Method

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A. Andargie and Y.N. Reddy, Fitted Fourth order tridiagonal finite difference method for singular perturbation problems, Appl. Math. Comp. 192 (2007), 90–100.

A. Ashyralyev and H.O. Fattorini, On uniform difference Schemes for second order singular perturbation problems in Banach spaces, SIAM J. Math. Anal. 23 (1992), 29–54.

E. Babolian and A. Shahsawaran, Numerical solution of nonlinear Fredholm integral equation of second kind using Haar wavelets, J. Comp. Appl. Math. 225 (2009), 87–95.

R.K. Bawa, Spline based Computational technique for linear singularly perturbed boundary value problems, Appl. Math. Comp. 167 (2005), 225–236.

R.C. Chin and R. Krasnay, A hybrid asymptotic finite element method for stiff two point boundary value problems, SIAM J. Sci. Stat. Comp. 4 (1983), 229–243.

W. Eckhaus, Asymptotic Analysis of Singular Perturbations, North Holland, New York (1979).

E.R. EI-Zahar, Approximate analytical solutions of singularly perturbed fourth order boundary value problems using differential transform method, J. Saud., Uni. Sci. 133 (2013), 257–265.

J.C. Goswami and C. Chan, Fundamentals of Wavelets, Theory, Algorithms and Applications, John Wiley and Sons, New York (1999).

A. Haar, Zur Theorie der orthogonalen Funktionenssysteme, (Erste Mitteilung), Mathematische Annalem 69 (1910), 31–37.

M.K. Kadalbajoo and D. Kumar, Variable mesh finite difference method for self-adjoint singularly perturbed two point boundary value problems, J. Comp. Math. 28 (2010), 711–724.

M.K. Kadalbajoo and V.K. Aggarwal, Fitted mesh B-spline collocation method for solving self-adjoint singularly perturbed boundary value problems, Appl. Math. Comp. 161 (2005), 973–987.

U. Lepik, Numerical solution of differential equation using Haar wavelets, Math. Comp. Simul. 68 (2005), 127–143.

R.K. Lodhi and H.K. Mishra, Solution of a class of fourth order singular singularly perturbed boundary value problems by quintic B-spline method, J. Nig. Math. Soc. 35 (2016), 257–265.

S. Mallat, A Wavelet Tour of Signal Processing, 2nd ed., Academic Press, New York (1999).

H.K. Mishra, M. Kumar and P. Singh, Initial value technique for self-adjoint singular perturbation boundary value problems, Comp. Math. Model. 20 (2009), 336–337.

R.E. O’Malley, Introduction to Singular Perturbations, Academic Press, New York (1974).

S.C. Rao and M. Kumar, Exponential B-spline collocation method for self-adjoint singularly perturbed boundary value problems, Appl. Num. Math. 58 (2008), 1572–1581.

Rashidinia, J.M. Ghasemi and Z. Mahmoodi, Spline approach to the solution of a singularly perturbed boundary value problems, Appl. Math. Comp. 189 (2007), 72–78.

Y.N. Reddy and P.P. Chakravarthy, Numerical patching method for singularly perturbed two point boundary value problems using cubic splines, Appl. Math. Comp. 147 (2004), 227–240.

E. Riordan and M.L. Pickett, Singularly perturbed problems modeling reaction-convection-diffusion process, Comp. Meth. Appl. Math. 3 (2003), 424–442.

K. Surla, Z. Uzelac and L. Teofanov, The discrete minimum principle for quadratic spline discretization of a singularly perturbed problem, Math. Comp. Simul. 79 (2009), 2490–2505.

V. Vukoslavecevic and K. Surla, Finite element method for solving self-adjoint singularly perturbed boundary value problems, Math. Montisnigri 8 (1996), 89–96.

DOI: http://dx.doi.org/10.26713%2Fjims.v9i3.818

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