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A body may have a structural, thermal, electromagnetic or optical role. In wave propagation, many models are described for transmission problems, whose solutions are defined in two or more domains. In this paper, we consider an inverse source hyperbolic problem on disconnected intervals, using solution point constraints. Applying a transform method, we reduce the inverse problems to direct ones, which are studied for well-posedness in special weighted Sobolev spaces. This means that the inverse problem is said to be well posed in the sense of Tikhonov (or conditionally well posed). The main aim of this study is to develop a finite difference method for solution of the transformed hyperbolic problems with a non-local differential operator and initial conditions. Numerical test examples are also analyzed. [ABSTRACT FROM AUTHOR]

Different from the construction process of the traditional finite difference method, we derive a large class of high-accuracy methods for approximating derivatives. Since Taylor expansion is avoided, the requirement for function smoothness in the new methods is greatly reduced. We analyze the approximation errors of the proposed methods and compare their approximation effects. As a typical application, we use the proposed methods to solve Elliptic, Hyperbolic and Parabolic problems numerically. For time-dependent problems, a class of new fully implicit difference schemes and the fourth-order Runge-Kutta method are both used for discretization. When using fully implicit difference schemes, unconditional stability and convergence are proved for hyperbolic and parabolic problems with the periodic boundary conditions. A large number of numerical experiments are provided to demonstrate the theoretical results. [ABSTRACT FROM AUTHOR]

The model of Timoshenko's shell theory of shells was used to analyze the dynamic characteristics of conical shells of variable thickness on a Pasternak elastic bed under nonstationary loading. Based on the Hamilton–Ostrogradsky variational principle, the equations of motion of a conical shell of variable thickness on a Pasternak elastic bed were derived. This system of hyperbolic differential equations is solved by the finite difference method. The numerical algorithm for solving the obtained equations is based on applying the integral-interpolation method for constructing difference schemes in the spatial coordinate and an explicit finite difference scheme for integration in the time coordinate. The influence of geometric dimensions, taper angle, and elastic media on the natural frequencies and other dynamic characteristics of a conical shell of variable thickness under the action of a pulsed load is analyzed using specific examples. New mechanical effects are revealed. [ABSTRACT FROM AUTHOR]