Parameter Estimation for Differential Equations

FUZZY INTEGRO-DIFFERENTIAL EQUATIONS: DISCRETE SOLUTION AND ERROR ESTIMATION

This paper investigates existence and uniqueness results for the first order fuzzy integro-differential equations. Then numerical results and error bound based on the left rectangular quadrature rule, trapezoidal rule and a hybrid of them are obtained. Finally an example is given to illustrate the performance of the methods.

Simulating and Forecasting OPEC Oil Price Using Stochastic Differential Equations

The main purpose of this paper is to provide a quantitative analysis to investigate the behavior of the OPEC oil price. Obtaining the best mathematical equation to describe the price and volatility of oil has a great importance. Stochastic differential equations are one of the best models to determine the oil price, because they include the random factor which can apply the effect of different ...

The use of radial basis functions by variable shape parameter for solving partial differential equations

In this paper, some meshless methods based on the local Newton basis functions are used to solve some time dependent partial differential equations. For stability reasons, used variably scaled radial kernels for constructing Newton basis functions. In continuation, with considering presented basis functions as trial functions, approximated solution functions in the event of spatial variable wit...

OPTIMIZATION AND SENSITIVITY ANALYSIS FOR MULTIRESPONSE PARAMETER ESTIMATION IN SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS by

Methodology for the simultaneous solution of ordinary differential equations (ODEs) and associated parametric sensitivity equations using the Decoupled Direct Method (DDM) is presented with respect to its applicability to multiresponse parameter estimation for systems described by nonlinear ordinary differential equations. The DDM is extended to provide second order sensitivity coefficients and...

A Parameter Uniform Numerical Scheme for Singularly Perturbed Differential-difference Equations with Mixed Shifts

In this paper, we consider a second-order singularly perturbed differential-difference equations with mixed delay and advance parameters. At first, we approximate the model problem by an upwind finite difference scheme on a Shishkin mesh. We know that the upwind scheme is stable and its solution is oscillation free, but it gives lower order of accuracy. So, to increase the convergence, we propo...

Lipari 2009 Biomathematics Summer School. Parameter Estimation in Physiological Models. Parameter Estimation for Stochastic Differential Equations from Noisy Observations. Maximum Likelihood and Filtering Techniques