Abstract We introduce new differentiation matrices based on the pseudospectral collocation method. Monic Chebyshev polynomials (MCPs) were used as trial functions in (D-matrices). Those have been to approximate solutions of higher-order ordinary differential equations (H-ODEs). Two techniques will be this work. The first technique is a direct approximation H-ODE. While second depends transformi...

Purpose A transient magneto-quasistatic vector potential formulation involving nonlinear material is spatially discretized using the finite element method of first and second polynomial order. By applying a generalized Schur complement resulting system differential algebraic equations reformulated into ordinary (ODE). The ODE integrated in time by explicit integration schemes. purpose this pape...

Semi-implicit multistep methods are an efficient tool for solving large-scale ODE systems. This recently emerged technique is based on modified Adams–Bashforth–Moulton (ABM) methods. In this paper, we introduce new semi-explicit and semi-implicit predictor–corrector the backward differentiation formula Adams–Bashforth We provide a thorough study of numerical stability performance compare their ...

Given the critical role played by natural gas in providing electricity, heat, and other essential services, better models are needed to understand dynamics of networks during extreme events. This paper aims at establishing appropriate fast simulation capture slow linepack depletion for ideal isothermal pipeline networks. Instead solving partial differential equations (PDE) on a large scale, thr...

Differential equations are extensively used for modeling dynamics of physical processes in many scientific fields such as engineering, physics, and biomedical sciences. Parameter estimation of differential equation models is a challenging problem because of high computational cost and high-dimensional parameter space. In this article, we propose a novel class of methods for estimating parameter...

In this paper, we propose a progressive Bayesian procedure, where the measurement information is continuously included into the given prior estimate (although we perform observations at discrete time steps). The key idea is to derive a system of ordinary first-order differential equations (ODE) by employing a new coupled density representation comprising a Gaussian density and its Dirac Mixture...

Although algebraic or so called “implicit polynomial” curves/surfaces have been studied rather extensively for several decades, to the best of our knowledge, a dynamic formulation of them, similar to active contours, has not been done yet. This paper proposes to use implicit polynomial functions instead of signed distance functions in classical level set formulation and shows potential of such ...

A method for model reduction in non-linear ODE systems is demonstrated through computational examples. The method does not require an implicit separation of time-scales in the fine dynamics to be effective. From the computational standpoint, the method has the potential of serving as a subgrid modeling tool. From the physical standpoint, it provides a model for interpreting and describing histo...

Code to recognise and hence solve the second-order linear ODEs that define the special functions of mathematical physics is being developed for the Reduce ODE solver. It allows an arbitrary, possibly symbolic, affine transformation of the independent variable. At first sight, the problem appears to be one of pattern matching or table look-up, but simple special-purpose code written for each cla...

The Jacobin doubly periodic wave solution, the Weierstrass elliptic function solution, the bell-type solitary wave solution, the kink-type solitary wave solution, the algebraic solitary wave solution, and the triangular solution of a generalized Korteweg-de Vries-modified Korteweg-de Vries equation (GKdV-mKdV) with higher-order nonlinear terms are obtained by a generalized subsidiary ordinary d...