Numerical solution of a boundary value problem for a loaded parabolic equation with nonlocal boundary conditions

В работе с использованием метода прямых исследуется численное решение краевой задачи относительно нагруженного параболического уравнения с нелокальными краевыми условиями. Получены расчетные формулы и приводится алгоритм для решения задачи. Приведены результаты численного решения двух тестовых задач, иллюстрирующие эффективность предложенного подхода In the work, we propose a numerical method of solution to the boundary-value problem with respect to the loaded parabolic equation with nonlocal boundary conditions. We have obtained formulas and derived an algorithm for the solution of the problem. We provide the results of numerical solution to two test problems, which illustrates the efficiency of the approach proposed.

Numerical Methods for Solving Physically Nonlinear Problems for Inhomogeneous Thick-Walled Shells

The paper proposes the numerical method of solution the problems of calculation the stress state in thick-walled cylinders and spheres from physically nonlinear inhomogeneous material. The urgency of solved problem due to the change of mechanical properties of materials under the influence of different physical fields (temperature, humidity, radiation, etc.). The deformation diagram describes the three-parameter formula. The numerical method used the method of successive approximations. The results of numerical calculation are compared with the test analytical solutions obtaining the authors with some restrictions on diagram parameters. The obtained results can be considered quite satisfactory.

An Efficient Numerical Algorithm for Solving Fractional Higher-Order Nonlinear Integrodifferential Equations

This paper is devoted to both theoretical and numerical study of boundary value problems for higher-order nonlinear fractional integrodifferential equations. Existence and uniqueness results for the considered problem are provided and proved. The numerical method of solution for the problem is based on a conjugate collocation and spline approach combined with shooting method. Some numerical examples are discussed to demonstrate the efficiency and the accuracy of the proposed algorithm.

The mathematical modelling and computer simulation of wildland fire perimeter growth over a 3-dimensional surface

This work considers wildfire growth over variable topography. Through an analysis of fire perimeter growth for homogeneous conditions over a surface of constant slope, a mathematical model of fire growth for heterogeneous conditions and variable surface is proposed. The mathematical model is in the form of a system of partial differential equations that require a numerical method of solution. A simple numerical solution technique is described and example solutions are given for fires over a variety of complex surfaces illustrating that simulation results can be obtained in reasonable time.