Legendre wavelet operational matrix method for solution of fractional order Riccati differential equation | ||||
| Journal of the Egyptian Mathematical Society | ||||
| Volume 23, Issue 2, 2015, Page 263-270 PDF (926.91 K) | ||||
| Document Type: Original Article | ||||
| DOI: 10.1016/j.joems.2014.04.007 | ||||
 View on SCiNiTO | ||||
| Author | ||||
| S. Balaji* | ||||
| Department of Mathematics, SASTRA University, Thanjavur 613 401, India | ||||
| Abstract | ||||
| A Legendre wavelet operational matrix method (LWM) presented for the solution of nonlinear fractional order Riccati differential equations, having variety of applications in engineering and applied science. The fractional order Riccati differential equations converted into a system of algebraic equations using Legendre wavelet operational matrix. Solutions given by the proposed scheme are more accurate and reliable and they are compared with recently developed numerical, analytical and stochastic approaches. Comparison shows that the proposed LWM approach has a greater performance and less computational effort for getting accurate solutions. Further existence and uniqueness of the proposed problem are given and moreover the condition of convergence is verified. | ||||
| Keywords | ||||
| Riccati equation; Non linear ODE; Fractional order differential equation; Legendre wavelet; Convergence criteria; Analytical approximation | ||||
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