𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Random Airy type differential equations: Mean square exact and numerical solutions

✍ Scribed by J.-C. Cortés; L. Jódar; F. Camacho; L. Villafuerte

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
326 KB
Volume
60
Category
Article
ISSN
0898-1221

No coin nor oath required. For personal study only.

✦ Synopsis

This paper deals with the construction of power series solutions of random Airy type differential equations containing uncertainty through the coefficients as well as the initial conditions. Under appropriate hypotheses on the data, we establish that the constructed random power series solution is mean square convergent over the whole real line. In addition, the main statistical functions, such as the mean and the variance, of the approximate solution stochastic process generated by truncation of the exact power series solution are given. Finally, we apply the proposed technique to several illustrative examples which show substantial speed-up and improvement in accuracy compared to other approaches such as Monte Carlo simulations.

📜 SIMILAR VOLUMES

Mean square power series solution of ran
Mean square power series solution of random linear differential equations
✍ G. Calbo; J.-C. Cortés; L. Jódar 📂 Article 📅 2010 🏛 Elsevier Science 🌐 English ⚖ 739 KB

This paper deals with the construction of random power series solutions of linear differential equations containing uncertainty through the diffusion coefficient, the source term as well as the initial condition. Under appropriate hypotheses on the data, we establish that the constructed random powe

Stability and oscillations of numerical
Stability and oscillations of numerical solutions for differential equations with piecewise continuous arguments of alternately advanced and retarded type
✍ Qi Wang; Qingyong Zhu; Mingzhu Liu 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 361 KB

This paper is concerned with the numerical properties of θ-methods for the solution of alternately advanced and retarded differential equations with piecewise continuous arguments. Using two θ -methods, namely the one-leg θ-method and the linear θ-method, the necessary and sufficient conditions unde

Numerical solution of Volterra integral
Numerical solution of Volterra integral and integro-differential equations of convolution type by using operational matrices of piecewise constant orthogonal functions
✍ E. Babolian; A. Salimi Shamloo 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 171 KB

In this paper, we use operational matrices of piecewise constant orthogonal functions on the interval [0, 1) to solve Volterra integral and integro-differential equations of convolution type without solving any system. We first obtain Laplace transform of the problem and then we find numerical inver