A family of high order product integration methods for an integral equation of Lighthill. (English) Zbl 0653.65094
M. J. Lighthill [Proc. R. Soc., Lond. Ser. A 202, 359-377 (1950; Zbl 0038.115)] has derived a nonlinear singular Volterra integral equation to describe the temperature distribution of the surface of a projectile moving through a laminar boundary layer at high Mach numbers. This paper presents high order product integration methods for its numerical solution and analyzes their convergence. Numerical results are given.
MSC:
| 65R20 | Numerical methods for integral equations |
| 76N20 | Boundary-layer theory for compressible fluids and gas dynamics |
| 45G05 | Singular nonlinear integral equations |
Keywords:
high accuracy; nonlinear singular Volterra integral equation; laminar boundary layer; product integration methods; convergence; Numerical resultsCitations:
Zbl 0038.115References:
| [1] | Anselone P. M., Nonlinear Integral Equations (1964) · Zbl 0149.11502 |
| [2] | Franco N. B. Soluçã o Numé rica de Algumas Equaç [otilde] es Integrais do Tipo Volterra Ph. D. thesis University of Sã o Paulo Brazil 1982 |
| [3] | Franco N. B., Matemá tica Aplicada e Computational 2 (3) pp 257– (1983) |
| [4] | Isaacson E., The Analysis of Numerical Methods (1966) · Zbl 0168.13101 |
| [5] | Lighthill, M. J. 1950.Proc. Roy. Soc.. Contributions to the theory of heat transfer through a laminar boundary layer. 1950. pp.359–377. · Zbl 0038.11504 |
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