Irina Perfilieva - University of Ostrava, Centre of Excellence IT۴Innovations, Institute for Research and Applications of Fuzzy Modeling, ۳۰. dubna ۲۲, ۷۰۱ ۰۳ Ostrava ۱, Czech Republic
Petra  Stevuliakova - University of Ostrava, Centre of Excellence IT۴Innovations, Institute for Research and Applications of Fuzzy Modeling, ۳۰. dubna ۲۲, ۷۰۱ ۰۳ Ostrava ۱, Czech Republic
Radek Valasek - University of Ostrava, Centre of Excellence IT۴Innovations, Institute for Research and Applications of Fuzzy Modeling, ۳۰. dubna ۲۲, ۷۰۱ ۰۳ Ostrava ۱, Czech Republic

We propose a fuzzy-based approach aiming at finding numerical solutions to some classical problems. We use the technique of F-transform to solve a second-order ordinary differential equation with boundary conditions. We reduce the problem to a system of linear equations and make experiments that demonstrate applicability of the proposed method. We estimate the order of accuracy of the proposed method. We show that the F-transform-based approach does not only extend the set of its applications, but has a certain advantage in the solution of ill-posed problems.

F-transform, Differential equation, Boundary value problem, Second order differential equation