Using the mathematical program Maple to solve mathematical physics problems by numerical methods

Abstract

The paper considers the application of mathematical program Maple to solve mathematical physics problems by numerical methods, such as a mixed boundary value problem for the string oscillation equation, the heat conduction equation and the Dirichlet problem for the Laplace equation. Although mixed boundary value problems have certain difficulties, there is a powerful arsenal of numerical methods and software tools that allow them to be solved. The example of the Maple software package shows not only obtaining a numerical solution, but also its visualization in the form of graphs and surfaces, which helps in understanding the behavior of the solution and the influence of various boundary conditions. Using Maple for numerical solution of mathematical physics problems allows computer science students and engineers to concentrate on the essence of the problem, they do not have to spend time on complex implementation of numerical algorithms. The writing of the numerical methods and conditions is quite clear, it is easy to change the equation parameters, initial/boundary conditions and mesh parameters for a quick study of the system behavior, the built-in algorithms are optimized and well-tested, which ensures the reliability of the calculations. The study of numerical methods involves their software implementation, which contributes to the development of programming skills, especially in the field of working with data sets, developing effective algorithms and optimizing the code. Specialists with a deep understanding of numerical methods are in demand in many industries, including IT companies, which is why when studying such methods we combine the use of the Maple mathematical package and software implementation in various programming languages