Stochastic differential equations (3rd ed.): an introduction with applications
Stochastic differential equations (3rd ed.): an introduction with applications
Mean square numerical solution of random differential equations: Facts and possibilities
Computers & Mathematics with Applications
Mathematical and Computer Modelling: An International Journal
Numerical solution of random differential equations: A mean square approach
Mathematical and Computer Modelling: An International Journal
Population growth as a nonlinear stochastic process
Mathematical and Computer Modelling: An International Journal
Computers & Mathematics with Applications
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In this paper we propose the numerical solutions of stochastic initial value problems via random Runge-Kutta methods of the second order and mean square convergence of these methods is proved. A random mean value theorem is required and established. The concept of mean square modulus of continuity is also introduced. Expectation and variance of the approximating process are computed. Numerical examples show that the approximate solutions have a good degree of accuracy.