# The Third Order Iterative Method for Solving Nonlinear Parabolic Equations and Its Application to the Biological Tissues Models

• I. F. Iumanova
• S. I. Solodushkin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11386)

## Abstract

We supply an iterative method for solving nonlinear difference schemes appearing after discretization of evolution partial differential equations. Proposed method is a kind of two stage iterative process, which does not use derivatives. The theorem of third order convergence is proven. Results of numerical experiments with test equations, which sources are equation from echocardiography, are presented.

## Keywords

Nonlinear difference scheme Acceleration of convergence Iterative method Echocardiography

## Notes

### Acknowledgments

We acknowledge the support by the program 02.A03.21.0006 on 27.08.2013 and the project Development of a personalized computer model of electrotherapy in heart failure patients with risk of sudden death MK-6328.2018.7.

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