Numerical Solution of First-Order Linear Differential Equations in Fuzzy Environment by Runge-Kutta-Fehlberg Method and Its Application

Table 1

Comparison of the exact solutions and numerical solutions for different step lengths at .

	Exact solution for (i)-gH differentiable case		Exact solution for (ii)-gH differentiable case		Numerical solution for by RKF method		⁢Numerical solution for by RKF method		⁢Numerical solution for by RKF method
	0	0.9686	1.0139	1.0558	1.1111	1.0597	1.1149	0.9696	1.0201	0.9610	1.0110
0.1	0.9723	1.0130	1.0602	1.1099	1.0642	1.1138	0.9737	1.0191	0.9650	1.0100
0.2	0.9759	1.0121	1.0646	1.1088	1.0686	1.1127	0.9777	1.0181	0.9690	1.0090
0.3	0.9795	1.0112	1.0691	1.1077	1.0730	1.1116	0.9818	1.0171	0.9730	1.0080
0.4	0.9831	1.0103	1.0735	1.1066	1.0774	1.1105	0.9858	1.0161	0.9770	1.0070
0.5	0.9867	1.0094	1.0779	1.1055	1.0818	1.1094	0.9898	1.0151	0.9810	1.0060
0.6	0.9904	1.0085	1.0823	1.1044	1.0862	1.1083	0.9939	1.0141	0.9850	1.0050
0.7	0.9940	1.0076	1.0867	1.1033	1.0906	1.1072	0.9979	1.0131	0.9890	1.0040
0.8	0.9976	1.0066	1.0912	1.1022	1.0951	1.1061	1.0020	1.0121	0.9930	1.0030
0.9	1.0012	1.0057	1.0956	1.1011	1.0995	1.1050	1.0060	1.0110	0.9970	1.0020
1	1.0048	1.0048	1.1000	1.1000	1.1039	1.1039	1.0100	1.0100	1.0010	1.0010