Think globally, act locally: solving highly-oscillatory ordinary differential equations
Applied Numerical Mathematics
Random Airy type differential equations: Mean square exact and numerical solutions
Computers & Mathematics with Applications
Epidemic models with random coefficients
Mathematical and Computer Modelling: An International Journal
Using Homotopy WHEP technique for solving a stochastic nonlinear diffusion equation
Mathematical and Computer Modelling: An International Journal
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The aim of this paper is twofold. First, we deal with the extension to the random framework of the piecewise Frobenius method to solve Airy differential equations. This extension is based on mean square stochastic calculus. Second, we want to explore the capability to provide not only reliable approximations for both the average and the standard deviation functions associated to the solution stochastic process, but also to save computational time as it happens in dealing with the analogous problem in the deterministic scenario. This includes a comparison of the numerical results with respect to those obtained by other commonly used operational methods such as polynomial chaos and Monte Carlo simulations. To conduct this comparative study, we have chosen the Airy random differential equation because it has highly oscillatory solutions. This feature allows us to emphasize differences between all the considered approaches.