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Mathematical models of various natural processes are described by differential equations, systems of partial differential equations and integral equations. In most cases, the exact solution to such problems cannot be determined; therefore, one has to use grid methods to calculate an approximate solution using high-performance computing systems. These methods include the finite element method, the finite difference method, the finite volume method and combined methods. In this Special Issue, we bring to your attention works on theoretical studies of grid methods for approximation, stability and convergence, as well as the results of numerical experiments confirming the effectiveness of the developed methods. Of particular interest are new methods for solving boundary value problems with singularities, the complex geometry of the domain boundary and nonlinear equations. A part of the articles is devoted to the analysis of numerical methods developed for calculating mathematical models in various fields of applied science and engineering applications. As a rule, the ideas of symmetry are present in the design schemes and make the process harmonious and efficient.
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Keywords
- boundary value problems with degeneration of the solution on entire boundary of the domain
- Brinkman penalization
- Continuity
- direct and inverse problems
- discontinuous Galerkin methods
- Economics, finance, business & management
- embedded geometry
- FEPG
- finite integration method
- Hermitian/skew-Hermitian splitting method
- high-order boundary
- High-order methods
- IMEX Runge–Kutta methods
- Industry & industrial studies
- Information technology industries
- interpolation
- invariantized difference scheme
- jaw crusher
- lie symmetries
- Media, information & communication industries
- multigrid methods
- Numerical solutions
- positivity-preserving
- quartic spline
- scattered data
- shifted Chebyshev polynomial
- skew-Hermitian triangular splitting method
- special graded mesh
- strongly non-Hermitian matrix
- surface reconstruction
- symmetrical laser cladding path
- the method of finite elements
- Tikhonov regularization method
- Triangulation
- Volterra integro-differential equation
- wear
Links
DOI: 10.3390/books978-3-0365-0377-6Editions