Abstract
In this paper, approximate solutions of second-order linear differential equations with fuzzy boundary conditions, in which coefficient functions maintain the sign, are investigated. The fuzzy linear boundary value problem is converted to a crisp function system of linear equations by the undetermined fuzzy coefficients method. The fuzzy approximate solution of the fuzzy linear differential equation is obtained by solving the crisp linear equations. Some numerical examples are given to illustrate the proposed method.
Highlights
1 Introduction Nowadays, fuzzy differential equations (FDEs) is a popular topic studied by many researchers since it is utilized widely for the purpose of modeling problems in science and engineering
Most of the practical problems require the solution of a fuzzy differential equation (FDE) which satisfies fuzzy initial or boundary conditions, a fuzzy initial or boundary problem should be solved
Fuzzy approximate solutions were obtained by solving a crisp function extended system of linear equations
Summary
Fuzzy differential equations (FDEs) is a popular topic studied by many researchers since it is utilized widely for the purpose of modeling problems in science and engineering. We discuss the approximate solution of the second-order fuzzy linear differential function boundary value problem. We obtain the fuzzy approximate solution of the original fuzzy linear differential equation as follows: y(t, r) = θ (r)φ (t) + θ (r)φ (t) + · · · + θ N (r)φN (t), y(t, r) = θ (r)φ (t) + θ (r)φ (t) + · · · + θ N (r)φN (t). Consider the following second-order fuzzy linear differential equation:. For some r ∈ [ , ]; all data were calculated by Matlab .x. Form Tables , , , , and , we know that the approximate solutions obtained from the proposed method are best close to the exact solutions of original linear deferential equations with fuzzy boundary value conditions
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