## Numerical solution of two transcendental equations

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- by Luciano Misici PDF
- Math. Comp.
**42**(1984), 589-595 Request permission

## Abstract:

This paper deals with the study of the transcendental equations: $\sin (s + v)/(s + v) = \pm \sin (s - v)/(s - v)$, where $v = {({s^2} - {\gamma ^2})^{1/2}}$. 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.## References

- 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**443511**, DOI 10.1137/0133021
L. M. de Socio & L. Misici, "Convezione in un mezzo poroso causata da sorgenti di calore," - James A. Ward,
*The down-hill method of solving $f(z)=0$*, J. Assoc. Comput. Mach.**4**(1957), 148–150. MR**92227**, DOI 10.1145/320868.320873
J. A. Bach, "On the downhill method,"

*Aereotecnica Missili e Spazio*, v. 60, no. 4, 1980, pp. 201-206. 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. H. C. Brinkman, "On the permeability of media consisting of closely packed porous particles,"

*Appl. Sci. Res.*, v. A1, 1947, pp. 81-86. 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. G. H. Hardy, "On the zeros of the integral function $x - \sin x$,"

*Messenger Math. n.s.*, v. 31, 1902, pp. 161-165.

*Comm. ACM*, v. 12, 1969, pp. 675-677.

## Additional Information

- © Copyright 1984 American Mathematical Society
- 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