The variable order wave equation plays a major role in acoustics, electromagnetics, and fluid dynamics. In this paper, we consider the space-time variable order fractional wave equation with variable coefficients. We propose an effective numerical method for solving the aforementioned problem in a bounded domain. The shifted Jacobi polynomials are used as basis functions, and the variable-order...

Since proposed in Zhang and Shu (2010) [1], the Zhang–Shu framework has attracted extensive attention motivated many bound-preserving (BP) high-order discontinuous Galerkin finite volume schemes for various hyperbolic equations. A key ingredient is decomposition of cell averages numerical solution into a convex combination values at certain quadrature points, which helps to rewrite as combinati...

Measurement of transient pressure distribution on maritime structures is important for the assessment hydrodynamic loads applied. The commonly used sensors are mostly bulky, need to be bolted structure, and/or only provide point-wise measurements. In this paper, an elastic matrix layer with a network embedded piezoelectric proposed address these issues. For experimental validation, 400 × 5 mm e...

Lagrangian systems with ideal nonholonomic constraints can be expressed as implicit index 2 differential-algebraic equations (DAEs) and can be derived from the Lagrange-d’Alembert principle. We define a new nonholonomically constrained discrete Lagrange-d’Alembert principle based on a discrete Lagrange-d’Alembert principle for forced Lagrangian systems. Nonholonomic constraints are considered a...

In this paper, a high-order moment-based multi-resolution Hermite weighted essentially non-oscillatory (HWENO) scheme is designed for hyperbolic conservation laws. The main idea of derived from our previous work [J. Comput. Phys., 446 (2021) 110653], in which the integral averages function and its first order derivative are used to reconstruct both values at boundaries. However, only Gauss-Loba...

This paper concerns a class of deferred correction methods recently developed for initial value ordinary differential equations; such methods are based on a Picard integral form of the correction equation. These methods divide a given timestep [tn, tn+1] into substeps, and use function values computed at these substeps to approximate the Picard integral by means of a numerical quadrature. The m...

In this paper, a new class of Runge–Kutta-type collocation methods for the numerical integration ordinary differential equations (ODEs) is presented. Its derivation based on integral form equation. The approach enables enhancing accuracy established Runge–Kutta while retaining same number stages. We demonstrate that, with proposed approach, Gauss–Legendre and Lobatto IIIA can be derived that th...