Numerical Solution of Singularly Perturbed Two-point BVPs Using Nonuniform Haar Wavelets

REFERENCES

• Boglaev , I. P. 1981 . A Variational Difference Scheme for a Boundary-value Problem with a Small Parameter in the Highest Derivative . U.S.S.R. Comput. Math. Phys. , 21 ( 4 ) : 71 – 81 .
   Google Scholar
• Dubeau , F. , Elmejdani , S. and Ksantini , R. 2004 . Nonuniform Haar Wavelets . Appl. Math. Comput. , 159 : 675 – 693 .
   Google Scholar
• Kadalbajoo , M. K. and Bawa , R. K. 2002 . Variable-mesh Difference Scheme for Singularly-perturbed Boundary-value Problems Using Splines . J. Optim. Theory , 9 : 405 – 416 .
   Google Scholar
• Kadalbajoo , M. K. and Patidar , K. C. 2002 . Numerical Solution of Singularly Perturbed Non-linear Two Point Boundary Value Problems by Spline in Compression . Inter. J. Computer Math. , 79 ( 2 ) : 271 – 288 .
   Web of Science ®Google Scholar
• Kadalbajoo , M. K. and Patidar , K. C. 2002 . A Survey of Numerical Techniques for Solving Singularly-perturbed Ordinary Differential Equations . Appl. Math. Comput. , 130 : 457 – 510 .
   Web of Science ®Google Scholar
• Kadalbajoo , M. K. and Patidar , K. C. 2006 . ε-uniformly Convergent Fitted Mesh Fintite Difference Methods for General Singular Perturbation Problems . Appl. Math. Comput. , 179 : 248 – 266 .
   Web of Science ®Google Scholar
• Khan , A. , Khan , I. and Aziz , T. 2006 . Sextic Spline Solution of a Singularly Perturbed Boundary-value Problems . Appl. Math. Comput. , 181 : 432 – 439 .
   Web of Science ®Google Scholar
• Kumar , M. , Mishra , H. K. and Singh , P. 2009 . Boundary Value Approch for a Class of Linear Singularly Perturbed Two-point Boundary-value Problems . Advances Engg. Soft. , 40 : 298 – 304 .
   Web of Science ®Google Scholar
• Kumar , M. and Singh , N. 2009 . A Collection of Computational Techniques for Solving Singular Boundary-value Problems . Advances Engg. Soft. , 40 : 288 – 297 .
   Google Scholar
• Kumar , V. and Mehra , M. 2009 . Wavelet Optimized Finite Difference Method Using Interpolating Wavelets for Self-adjoint Singularly Perturbed Problems . J. Comput. Appl. Math. , 230 : 803 – 812 .
   Google Scholar
• Lepik , Ü . 2008 . Solving Integral and Differential Equations by the Aid of Nonuniform Haar Wavelets . Appl. Math. Comput. , 198 : 326 – 332 .
   Web of Science ®Google Scholar
• Lin , B. , Li , K. and Cheng , Z. 2009 . B-spline Solution of a Singularly Perturbed Boundary Value Problem Arising in Biology . Chaos, Solitons and Fractals , 42 ( 5 ) : 2934 – 2948 .
   Google Scholar
• Mohanty , R. K. and Jha , N. 2005 . A Class of Variable Mesh Spline in Compression Methods for Singularly Perturbed Two-point Singular Boundary-value Problems . Appl. Math. Comput. , 168 : 704 – 716 .
   Web of Science ®Google Scholar
• Natesan , S. and Ramanujam , N. 1999 . Improvement of Numerical Solution of Self-adjoint Singular Perturbation Problems by Incorporation of Asymptotic Approximations . Appl. Math. Comput. , 98 : 119 – 137 .
   Web of Science ®Google Scholar
• Niijima . 1980 . On a Three Point Difference Scheme for a Singular Perturbation Problem Without a First Derivative Term . I. Mem. Numer. Math. , 7 : 1 – 10 .
   Google Scholar
• O’Riordan , E. and Stynes , M. 1986 . A Uniformly Uccurate Uinite Ulement Uethod for a Uingularly Uerturbed One-dimensional Reaction Diffusion Problem . Math. Comput. , 47 ( 4 ) : 555 – 570 .
   Google Scholar
• Radunovic , D. 2007 . Spline-Wavelet Solution of Singularly Perturbed Boundary Problem . Matematiqki Vesnik , 59 : 31 – 46 .
   Google Scholar
• Rao , S.C. S. and Kumar , M. 2008 . Exponential B-spline Collocation Method for Self-adjoint Singularly Perturbed Boundary Value Problems . Applied Numerical Mathematics , 58 : 1572 – 1581 .
   Google Scholar
• Shishkin , G. I. 1983 . A Difference Scheme on a Non-uniform Mesh for a Differential Equation with a Small Parameter in the Highest Derivative . U.S.S.R. Comput. Math. Phys. , 23 ( 3 ) : 59 – 66 .
   Google Scholar
• Surla , K. , Herceg , D. and Cvetkovic , L. 1991 . A Family of Exponential Spline Difference Schemes, Review of Research, Faculty of Science . Mathematics Series, University of Novi Sad , 19 : 12 – 23 .
   Google Scholar
• Surla , K. and Stojanovic , M. 1988 . Solving Singularly-perturbed Boundary-value Problems by Splines in Tension . J. Comput. Appl. Math. , 24 : 355 – 363 .
   Web of Science ®Google Scholar
• Surla , K. and Vukoslavcevic , V. 1995 . A Spline Difference Scheme for Boundary-value Problems with a Small Parameter . Review of Research, Faculty of Science, Mathematics Series, University of Novi Sad , 25 : 159 – 166 .
   Google Scholar
• Vukoslavcevic , V. and Surla , K. 1996 . Finite Element Method for Solving self-adjoint Singularly Perturbed Boundary-value Problems . Math. Montisnigri , 7 : 86 – 89 .
   Google Scholar