A note on the convergence of fuzzy transformed finite difference methods

Abstract

In this paper, we develop numerical methods based on the fuzzy transform methods (FTMs). In this approach we apply fuzzy transforms on discrete version of the derivatives and use it to derive FTMs. We also establish convergence of the proposed FTMs. To test the efficiency of the proposed FTMs, we apply the FTM schemes on the second order nonlinear singular boundary value problems and fourth order BVPs. We allow the source term of the differential equation to have jump discontinuity and study the effect of jump on FTMs and finite difference methods. The work shows that FTMs are better for both class of BVPs considered in this paper, having singularity, nonlinearity and jump discontinuity.