A numerical scheme with adaptive stepsize for Stochastic Differential Equations with additive noise
DOI:
https://doi.org/10.5540/03.2023.010.01.0012Palavras-chave:
stochastic differential equations, A-stability, variable stepsize methods, local linearizationResumo
This paper introduces an A-stable adaptive integrator based on the Local Linearization (LL) technique for the computer simulation of stochastic differential equations driven by additive noise. To construct the method, novel embedding stochastic LL schemes and a adaptive strategy are proposed. Simulation results are presented to illustrate the practical performance of the introduced integrator.
Downloads
Referências
Pamela Marion Burrage and Kevin Burrage. “A Variable Stepsize Implementation for Stochastic Differential Equations”. In: SIAM Journal on Scientific Computing 24.3 (2002), pp. 848–864.
Hugo de la Cruz et al. “Local Linearization Runge–Kutta methods: A class of A-stable explicit integrators for dynamical systems”. In: Mathematical and Computer Modelling 57.3 (2013), pp. 720–740.
Hugo De la Cruz et al. “A higher order local linearization method for solving ordinary differential equations”. In: Applied mathematics and computation 185.1 (2007), pp. 197–212.
Hugo De la Cruz Cancino et al. “High order local linearization methods: An approach for constructing A-stable explicit schemes for stochastic differential equations with additive noise”. In: BIT Numerical Mathematics 50 (2010), pp. 509–539.
Pablo Aguiar De Maio. “Um método de linearização local com passo adaptativo para solução numérica de equações diferenciais estocásticas com ruído aditivo”. Master dissertation. Escola de Matemática Aplicada da Fundação Getúlio Vargas, 2015.
Juan Carlos Jimenez, Hugo de la Cruz, and Pablo Aguiar De Maio. “Efficient computation of phi-functions in exponential integrators”. In: Journal of Computational and Applied Mathematics 374 (2020), p. 112758.
Juan Carlos Jimenez and Hugo de la Cruz Cancino. “Convergence rate of strong Local Linearization schemes for stochastic differential equations with additive noise”. In: BIT Numerical Mathematics 52.2 (2012), pp. 357–382.
Peter E Kloeden and Eckhard Platen. Numerical Solution of Stochastic Differential Equations. Springer, 1999.
