DOI: https://doi.org/10.36719/2663-4619/114/280-289
Zohra Gurbanova
Azerbaijan State Oil and Industry University
Master student
https://orcid.org/0009-0006-7108-4071
znftullayeva@gmail.com
Identification of the Right Side of the Parabolic Equation Depending
on Spatial Variables
Abstract
An iterative conjugate gradient method was proposed for the numerical solution of the inverse problem related to the determination of the multiplier of the right side of the parabolic equation depending on the spatial variables; A calculation algorithm was developed for the simultaneous determination of the lowest (most significant) coefficient and multiplier of the right side of the parabolic equation as a function of time. The method consists of providing an approximate solution in the upper time layer in the form of a linear combination of three boundary value problems for the elliptic equation; A numerical method based on the superposition of the solutions of two boundary value problems for second-order ordinary differential equations is proposed to numerically solve the continuation problem for the parabolic equation.
New numerical methods based on the relation of local radial basis functions are proposed to numerically solve the retrospective inverse heat conduction problem in the field of irregular computation.
Corresponding numerical examples show that the proposed new methods are effective.
Keywords: parabolic equations, parameter, variable, method, difference analog, inverse problem