Haar wavelet method for solving stiff differential equations

References

• Abelman , S. and Patidar , K.C. 2008 . Comparison of some recent numerical methods for initial‐value problems for stiff ordinary differential equations . Comput. Math. with Applications, , 55 : 733 – 744 . (doi:10.1016/j.camwa.2007.05.012)
   Web of Science ®Google Scholar
• Bujurke , N.M. , Salimath , C.S. and Shirashetti , S.C. 2008 . Numerical solution of stiff systems from nonlinear dynamics using single‐term Haar wavelet series . Nonlinear Dynamics, , 51 : 595 – 605 . (doi:10.1007/s11071–007–9248–8)
   Web of Science ®Google Scholar
• Celik , E. 2004 . On the numerical solution of differential‐algebraic equations with index ‐ 2 . Appl. Math. Comp., , 156 : 541 – 550 . (doi:10.1016/j.amc.2003.08.018)
   Web of Science ®Google Scholar
• Enright , W.H. , Hull , T.E. and Lindberg , B. 1975 . Comparing numerical methods for stiff systems of ODEs . BIT, , 15 (1) : 10 – 48 . (doi:10.1007/BF01932994)
   Google Scholar
• Gao , J. and Jiang , Y.‐L. 2007 . An adaptive wavelet method for nonlinear differential‐algebraic equations . Appl. Math. Comp., , 189 : 208 – 220 . (doi:10.1016/j.amc.2006.11.102)
   Web of Science ®Google Scholar
• Guzel , N. and Bayram , M. 2005 . On the numerical solution of stiff systems . Appl. Math. Comp., , 170 : 230 – 236 . (doi:10.1016/j.amc.2004.11.035)
   Web of Science ®Google Scholar
• Hairer , E. and Wanner , G. 1991 . Solving Ordinary Differential Equations II: Stiff and Differential‐Algebraic Problems. , Springer‐Verlag .
   Google Scholar
• Hojjati , G. , Rahimi , M.Y. , Ardabili and Hosseini , S.M. 2004 . A‐EBDF: an adaptive method for numerical solution of stiff systems of ODEs . Math. Computers in Simulation, , 66 : 33 – 41 . (doi:10.1016/j.matcom.2004.02.019)
   Web of Science ®Google Scholar
• Hsiao , C.‐H. 2004 . Haar wavelet approach to linear stiff systems . Math. Computers in Simulation, , 64 : 561 – 567 . (doi:10.1016/j.matcom.2003.11.011)
   Web of Science ®Google Scholar
• Hsiao , C.‐H. 2005 . Numerical solution of stiff differential equations via Haar wavelets . Int. J. Comp. Math., , 82 (9) : 1117 – 1123 . (doi:10.1080/00207160512331323308)
   Web of Science ®Google Scholar
• Hsiao , C.‐H. and Wang , W.‐J. 2001 . Haar wavelet approach to nonlinear stiff systems . Math. Computers in Simulation, , 57 : 347 – 353 . (doi:10.1016/S0378–4754(01)00275–0)
   Web of Science ®Google Scholar
• Lepik , Ü. 2006 . Haar wavelet method for nonlinear integro‐differential equations . Appl. Math. Comput., , 176 : 324 – 333 . (doi:10.1016/j.amc.2005.09.021)
   Web of Science ®Google Scholar
• Lepik , Ü. 2007 . Numerical solution of evolution equations by the Haar wavelet method . Appl. Math. Comput., , 185 (1) : 695 – 704 . (doi:10.1016/j.amc.2006.07.077)
   Web of Science ®Google Scholar
• Lepik , Ü. 2008 . Solving differential and integral equations by the Haar wavelet method; revisited . Int. J. Math. Comput., , 1 : 43 – 52 .
   Google Scholar
• Lepik , Ü. 2008 . Solving integral and differential equations by the aid of nonuniform Haar wavelets . Appl. Math. Comput., , 198 : 326 – 332 . (doi:10.1016/j.amc.2007.08.036)
   Web of Science ®Google Scholar
• Mahmood , A.S. , Casasús , L. and Al‐Hayani , W. 2005 . The decomposition method for stiff systems of ordinary differential equations . Appl. Math. Comp., , 167 : 964 – 975 . (doi:10.1016/j.amc.2004.06.134)
   Web of Science ®Google Scholar
• Press , W.H. , Flannery , B.P. , Teukolsky , S.A. and Vetterling , W.T. 1987 . Numerical Recipes. , Cambridge University Press .
   Google Scholar
• Shacham , M. and Brauner , N. 2008 . Preventing oscillatory behavior in error control for ODEs . Comput. Chem. Engng, , 32 : 409 – 419 . (doi:10.1016/j.amc.2004.06.134)
   Web of Science ®Google Scholar
• Tade , M. and Zhang , T. 2008 . Wavelet approach incorporated with optimization for solving stiff systems . J. Math. Chem., , 43 : 1553 – 1548 .
   Web of Science ®Google Scholar
• Tian , Y.‐C. and Zhang , T. 2008 . Wavelet‐based collocation method for stiff systems in process engineering . J. Math. Chem., , 44 : 501 – 513 . (doi:10.1007/s10910–007–9324–9)
   Web of Science ®Google Scholar
• Vijalapura , P.K. , Strain , J. and Covindjee , S. 2005 . Fractional step methods for index ‐ 1 differential‐algebraic equations . J. Comput. Phys., , 203 : 305 – 320 . (doi:10.1016/j.jcp.2004.08.015)
   Web of Science ®Google Scholar