Numerical solutions of fuzzy differential equations
The authors study the explicit Euler approximation of a Cauchy problem for fuzzy (ordinary) differential equations. By the embedding approach, the original problem in a Banach space with supremum norm is replaced by two parametric, first-order ordinary differential equations. These differential equations can be solved by classical numerical algorithms. The authors present a pointwise convergence theorem for the standard Euler method in the given Banach space under uniform boundedness of second derivatives, Lipschitz-continuous right hand sides and for equidistant stepsize selection. 5 examples (both linear and nonlinear) are exhibited and discussed in view of the implementation of the explicit Euler approximation. A standard, two-dimensional error estimation is given in terms of the global Lipschitz constant, the length of integration interval \(T-t_0\), and the equidistant stepsize \(h\).
scientific article; zbMATH DE number 1339611