This tutorial introduces some basic numerical computation techniques that are useful for the simulation and analysis of complex systems modelled by differential equations. Such differential models, especially those partial differential ones, have been extensively used in various areas from astronomy to biology, from meteorology to finance. However, if we ignore the differences caused by applica...

BACKGROUND Ureteropelvic junction obstruction (UPJO) is one of the most common causes of urinary tract obstruction in children. Several methods are used to diagnose upper urinary tract obstruction including renal ultrasonography (US), intravenous pyelogram (IVP), diuretic renography (DR), magnetic resonance urography (MRU) and antegrade or retrograde pyelography. Nowadays it is suggested to use...

In this paper, a new approach for solving the second order fuzzy differential equations (FDE) with fuzzy initial value, under strongly generalized H-differentiability is presented. Solving first order fuzzy differential equations by extending 1-cut solution of the original problem and solving fuzzy integro-differential equations has been investigated by some authors (see for example cite{darabi...

For systems of coupled differential equations on a sequence of W -random graphs, we derive the continuum limit in the form of an evolution integral equation. We prove that solutions of the initial value problems (IVPs) for the discrete model converge to the solution of the IVP for its continuum limit. These results combined with the analysis of nonlocally coupled deterministic networks in Medve...

The aim of this study was to compare non-enhanced spiral CT (NECT) and intravenous pyelography (IVP) in patients with suspected acute renal colic. Two-hundred patients presenting to the Emergency Department with suspected acute renal colic were randomized into groups undergoing NECT or IVP. The main outcome measures were diagnostic utility, incidence of alternative diagnoses, requirement for fu...

In many applications, there is a need to choose mathematical models that depend on non-smooth functions. The task of simulation becomes especially difficult if such functions appear on the right-hand side of an initial value problem. Moreover, solution processes from usual numerics are sensitive to roundoff errors so that verified analysis might be more useful if a guarantee of correctness is r...

PVODE is a high-performance ordinary diierential equation solver for the types of initial value problems (IVPs) that arise in large-scale computational simulations. Often, one wants to compute sensitivities with respect to certain parameters in the IVP. We discuss the use of automatic diierentiation (AD) to compute these sensitivities in the context of PVODE. Results on a simple test problem in...

The present work approaches the problem of achieving the approximate solution of the second order initial value problems (IVPs) via its conversion into a Volterra integral equation of the second kind (VIE2). Therefore, we initially solve the IVPs using Runge–Kutta of the forth–order method (RK), and then convert it into VIE2, and apply the εmodified block–pulse functions (εMBPFs) and their oper...

This paper focuses on the derivation, analysis and implementation of a hybrid method by optimizing order introduction six-hybrid points for direct solution fifth ordinary differential equations initial value problems (IVPs). Power series was used as basis function IVP. The interpolated at some selected whereas derivative approximate collocated all interval integration to generate system linear ...