# Difference Schemes for the Nonlinear Equations in Partial Derivatives with Heredity

• T. V. Gorbova
• V. G. Pimenov
• S. I. Solodushkin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11386)

## Abstract

We consider the initial-boundary value problem for nonlinear partial differential equations, the source of which are population models. Nonlinearity is contained both in the differential operator and in the inhomogeneity function. We construct a nonlinear implicit difference scheme, which requires the use of iterative solution methods on each time layer. Stability and convergence of the proposed numerical method were proved. Numerical experiments have been carried out, both on test examples and on the example of the biological model of the population.

## Keywords

Nonlinear difference scheme Convergence of the difference scheme Partial differential equation

## Notes

### Acknowledgments

We acknowledge the support by the program 02.A03.21.0006 on 27.08.2013.

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## Authors and Affiliations

• T. V. Gorbova
• 1
• V. G. Pimenov
• 1
• 2
• S. I. Solodushkin
• 1
• 2
Email author
1. 1.Ural Federal UniversityEkaterinburgRussia
2. 2.Institute of Mathematics and MechanicsUral Branch of the RASEkaterinburgRussia