*Correspondence: Raymond J. Spiteri, Numerical Simulation Laboratory, Department of Computer Science, University of Saskatchewan, 176 Thorvaldson Building, 110 Science Place, Saskatoon, SK S7N 5C9, Canada e-mail: [email protected] The bidomain model is a popular model for simulating electrical activity in cardiac tissue. It is a continuum-based model consisting of non-linear ordinary differen...

The FATODE, which is extracted from the KPP numerical libraray, is a Fortran programming library for the integration of stiff ODE systems. It incorporates a set of generic linear solvers suitable for large sparse systems. And the set allows users to add their own implementation conveniently. FATODE contains three families of methods – fully implicit Runge-Kutta methods, SDIRK methods and Rosenb...

Ordinary differential equations (ODEs), including high-order implicit equations, describe important problems in mechanical and chemical engineering. However, the use of selfvalidated methods providing rigorous enclosures of the solution has mostly been limited to explicit and weakly nonlinear problems, and no general-purpose algorithm for the validated integration of general ODE initial value p...

Abstract. We show that the fourth-order nonlinear ODE which controls the pole dynamics in the general solution of equation P 2 I compatible with the KdV equation exhibits two remarkable properties: (1) it governs the isomonodromy deformations of a 2× 2 matrix linear ODE with polynomial coefficients, and (2) it does not possess the Painlevé property. We also study the properties of the Riemann–H...

The propagation of electromagnetic waves in general media is modeled by the time-dependent Maxwell’s partial differential equations (PDEs), coupled with constitutive laws that describe the response of the media. In this work, we focus on nonlinear optical media whose response is modeled by a system of first order nonlinear ordinary differential equations (ODEs), which include a single resonance...

We develop backstepping state feedback control to stabilize a moving shockwave in freeway segment under bilateral boundary actuations of traffic flow. A shockwave, consisting light upstream the and heavy downstream, is usually caused by changes local road situations. The density discontinuity travels drivers caught experience transitions from free congested traffic. Boundary design this paper b...

Although algebraic or so-called “implicit polynomial” curves 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 develops a dynamic formulation for implicit polynomial curves based on level set formalism. In particular, it is shown that utilization of an implicit poly...

We analyze a time independent integral equation defined on a spatially extended domain which arises in the modeling of neuronal networks. In our survey, the coupling function is oscillatory and the firing rate is a smooth “heaviside-like” function. We will derive an associated fourth order ODE and establish that any bounded solution of the ODE is also a solution of the integral equation. We wil...