Numerical solution of two transcendental equations

Author:
Luciano Misici

Journal:
Math. Comp. **42** (1984), 589-595

MSC:
Primary 65H05; Secondary 65N25

DOI:
https://doi.org/10.1090/S0025-5718-1984-0736454-X

MathSciNet review:
736454

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Abstract: This paper deals with the study of the transcendental equations: , where . These equations are obtained in the study of some boundary value problems for a modified biharmonic equation using the Papkovich-Fadle series. Some numerical solutions obtained with an iterative procedure are given.

**[1]**Daniel D. Joseph,*The convergence of biorthogonal series for biharmonic and Stokes flow edge problems*, SIAM J. Appl. Math.**33**(1977), no. 2, 337–347. MR**0443511**, https://doi.org/10.1137/0133021**[2]**L. M. de Socio & L. Misici, "Convezione in un mezzo poroso causata da sorgenti di calore,"*Aereotecnica Missili e Spazio*, v. 60, no. 4, 1980, pp. 201-206.**[3]**H. C. Brinkman, "A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles,"*Appl. Sci. Res.*, v. A1, 1947, pp. 27-34.**[4]**H. C. Brinkman, "On the permeability of media consisting of closely packed porous particles,"*Appl. Sci. Res.*, v. A1, 1947, pp. 81-86.**[5]**L. M. de Socio, G. Gaffuri & L. Misici, "Stokes flow in a rectangular well. Natural convection and boundary layer function,"*Quart. Appl. Math.*, v. 39, 1982, pp. 499-508.**[6]**G. H. Hardy, "On the zeros of the integral function ,"*Messenger Math. n.s.*, v. 31, 1902, pp. 161-165.**[7]**James A. Ward,*The down-hill method of solving 𝑓(𝑧)=0*, J. Assoc. Comput. Mach.**4**(1957), 148–150. MR**0092227**, https://doi.org/10.1145/320868.320873**[8]**J. A. Bach, "On the downhill method,"*Comm. ACM*, v. 12, 1969, pp. 675-677.

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DOI:
https://doi.org/10.1090/S0025-5718-1984-0736454-X

Article copyright:
© Copyright 1984
American Mathematical Society