Semianalytic numerical studies of turning points arising in stiff boundary value problems

Authors:
W. L. Miranker and J. P. Morreeuw

Journal:
Math. Comp. **28** (1974), 1017-1034

MSC:
Primary 65L10

MathSciNet review:
0381329

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Abstract: A numerical algorithm for solving stiff boundary value problems with turning points is presented. The stiff systems are characterized as singularly perturbed differential equations. The numerical method is derived by appropriately discretizing the boundary layer and connection theory for such systems. Numerical results demonstrate the effectiveness of the method. In many cases the calculation proceeds with mesh increments which are orders of magnitude larger than those used by other known methods.

**[1]**Fred W. Dorr,*An example of ill-conditioning in the numerical solution of singular perturbation problems*, Math. Comp.**25**(1971), 271–283. MR**0297142**, 10.1090/S0025-5718-1971-0297142-0**[2]**F. W. Dorr, S. V. Parter, and L. F. Shampine,*Applications of the maximum principle to singular perturbation problems*, SIAM Rev.**15**(1973), 43–88. MR**0320456****[3]**A. M. Il′in,*A difference scheme for a differential equation with a small parameter multiplying the highest derivative*, Mat. Zametki**6**(1969), 237–248 (Russian). MR**0260195****[4]**W. L. Miranker,*Numerical methods of boundary layer type for stiff systems of differential equations*, Computing (Arch. Elektron. Rechnen)**11**(1973), no. 3, 221–234 (English, with German summary). MR**0386276****[5]**R. E. O'MALLEY,*Introduction to Singular Perturbation*, Lecture Notes at Edinburgh, Autumn, 1971.**[6]**Carl E. Pearson,*On a differential equation of boundary layer type*, J. Math. and Phys.**47**(1968), 134–154. MR**0228189**

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DOI:
https://doi.org/10.1090/S0025-5718-1974-0381329-5

Article copyright:
© Copyright 1974
American Mathematical Society