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In this paper we investigate overdetermined systems of scalar PDEs on the plane with one common characteristic, whose general solution depends on 1 function of 1 variable. We describe linearization of such systems and their integration via…
In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…
We introduce the linear operators of fractional integration and fractional differentiation in the framework of the Riemann-Liouville fractional calculus. Particular attention is devoted to the technique of Laplace transforms for treating…
The classical Talbot method for the computation of the inverse Laplace transform is improved for the case where the transform is analytic in the complex plane except for the negative real axis. First, by using a truncated Talbot contour…
In various provers and deductive verification tools, logical transformations are used extensively in order to reduce a proof task into a number of simpler tasks. Logical transformations are often part of the trusted base of such tools. In…
Complex vector analysis is widely used to analyze continuous systems in many disciplines, including physics and engineering. In this paper, we present a higher-order-logic formalization of the complex vector space to facilitate conducting…
Simulink is a graphical environment that is widely adapted for the modeling and the Laplace transform based analysis of linear analog circuits used in signal processing architectures. However, due to the involvement of the numerical…
In this paper we apply the innovative Laplace transformation method introduced by Sheen, Sloan, and Thom\'ee (IMA J. Numer. Anal., 2003) to solve the Black-Scholes equation. The algorithm is of arbitrary high convergence rate and naturally…
In this research work, let us focus on the construction of numerical scheme based on radial basis functions finite difference (RBF-FD) method combined with the Laplace transform for the solution of fractional order dispersive wave…
The deformation method of transformation optics has been demonstrated to be a useful tool, especially in designing arbitrary and nonsingular transformation materials. Recently, there are emerging demands for isotropic material parameters,…
We give a new procedure for generalized factorization and construction of the complete solution of strictly hyperbolic linear partial differential equations or strictly hyperbolic systems of such equations in the plane. This procedure…
The traditional theory of Laplace transformation in its currently prevalent form is unsatisfactory. Its deficiencies can be traced back to a mismatch of the definition intervals of the original function and of the inverse L-transform. A new…
We introduce a frequency-domain framework for convergence analysis of hyperparameters in game optimization, leveraging High-Resolution Differential Equations (HRDEs) and Laplace transforms. Focusing on the Lookahead algorithm--characterized…
Laplace transforms for integrals of stochastic processes have been known in analytically closed form for just a handful of Markov processes: namely, the Ornstein-Uhlenbeck, the Cox-Ingerssol-Ross (CIR) process and the exponential of…
The conserved densities of hydrodynamic type system in Riemann invariants satisfy a system of linear second order partial differential equations. For linear systems of this type Darboux introduced Laplace transformations, generalising the…
We present a method derived from Laplace transform theory that enables the evaluation of fractional integrals. This method is adapted and extended in a variety of ways to demonstrate its utility in deriving alternative representations for…
Synthetic Biology is an interdisciplinary field that utilizes well-established engineering principles, ranging from electrical, control and computer systems, for analyzing the biological systems, such as biological circuits, enzymes,…
Modelling forced dynamical systems - where an external input drives the system state - is critical across diverse domains such as engineering, finance, and the natural sciences. In this work, we propose Laplace-Net, a decoupled, solver-free…
Bond graph is a unified graphical approach for describing the dynamics of complex engineering and physical systems and is widely adopted in a variety of domains, such as, electrical, mechanical, medical, thermal and fluid mechanics.…
We introduce a transformation of linear Pfaffian systems, which we call the middle Laplace transform, as a formulation of the Laplace transform from the perspective of Katz theory. While the definition of the middle Laplace transform is…