Ill-Posed Problems

K.Saranya; Ms.N.Rajakumari

doi:https://doi.org/10.14445/22315373/IJMTT-V65I7P536

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 65 | Issue 7 | Year 2019 | Article Id. IJMTT-V65I7P536 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I7P536

Ill-Posed Problems

K.Saranya, Ms.N.Rajakumari

Citation :

K.Saranya, Ms.N.Rajakumari, "Ill-Posed Problems," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 7, pp. 306-314, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I7P536

Abstract

This process proposed to ill-posed problems in the field of mathematical physics and partial differential and integral equations, there are many simpler yet not less important ill-posed problems among algebraic equations, differential equations, extremum problems, etc. To avoid errors, prior to solving any problem it is recommended to check if the problem is a well-posed or ill-posed one. This journal aims to present original articles on the theory, numerics and applications of inverse and ill-posed problems. These inverse and ill-posed problems arise in mathematical physics and mathematical analysis, geophysics, acoustics, electrodynamics, tomography, medicine, ecology, financial mathematics etc.

Keywords

ill-posed problems, differential equations, roots of polynomials.

References

[1] Carl M. Bender, Steven A. Orszag, Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory, Springer, 1991.
[2] Heinz W. Engl, Martin Hanke and Andreas Neubauer, Regulariza- tion of Inverse Problems, Kluwer Academic Publishers, 1996.
[3] V. K. Ivanov, V. V. Vasin, V. P. Tanana, Theory of Linear Ill-posed Problems and its Applications, Walter De Gruyter GmbH and Co, 2002.
[4] A. Kirsch, An Introduction to the Mathematical Theory of Inverse Prob- lems, Springer-Verlag, New York, Inc, 1996.
[5] Peter Linz, A New Numerical Method for Ill-posed Problems, Inverse Prob- lems 10, L1-L6, 1994.
[6] Yu. P. Petrov, V. S. Sizikov, Well-posed, Ill-posed, and Intermediate Problems with Applications, Brill Academic Publishers, 2005.
[7] A. A. Samarskii, P. N. Vabishchevich, Numerical Methods for Solving Inverse Problems of Mathematical Physics, Walter De Gruyter GmbH and Co, 2000.