Müntz–Legendre Wavelet Collocation Method for Solving Fractional Riccati Equation
We propose a wavelet collocation method for solving the fractional Riccati equation, using the Müntz–Legendre wavelet basis and its associated operational matrix of fractional integration. The fractional Riccati equation is first transformed into a Volterra integral equation with a weakly singular k...
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MDPI AG
2025-03-01
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| author | Fatemeh Soleyman Iván Area |
| author_facet | Fatemeh Soleyman Iván Area |
| author_sort | Fatemeh Soleyman |
| collection | DOAJ |
| description | We propose a wavelet collocation method for solving the fractional Riccati equation, using the Müntz–Legendre wavelet basis and its associated operational matrix of fractional integration. The fractional Riccati equation is first transformed into a Volterra integral equation with a weakly singular kernel. By employing the collocation method along with the operational matrix, we reduce the problem to a system of nonlinear algebraic equations, which is then solved using Newton–Raphson’s iterative procedure. The error estimate of the proposed method is analyzed, and numerical simulations are conducted to demonstrate its accuracy and efficiency. The obtained results are compared with existing approaches from the literature, highlighting the advantages of our method in terms of accuracy and computational performance. |
| format | Article |
| id | doaj-art-4232e63ee305404b8eba61b848583c65 |
| institution | DOAJ |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-4232e63ee305404b8eba61b848583c652025-08-20T02:42:45ZengMDPI AGAxioms2075-16802025-03-0114318510.3390/axioms14030185Müntz–Legendre Wavelet Collocation Method for Solving Fractional Riccati EquationFatemeh Soleyman0Iván Area1K.N. Toosi University of Technology, Tehran P.O. Box 16315-1618, IranDepartamento de Matemática Aplicada II, IFCAE, Universidade de Vigo, E.E. Aeronáutica e do Espazo, Campus As Lagoas-Ourense, 32004 Ourense, SpainWe propose a wavelet collocation method for solving the fractional Riccati equation, using the Müntz–Legendre wavelet basis and its associated operational matrix of fractional integration. The fractional Riccati equation is first transformed into a Volterra integral equation with a weakly singular kernel. By employing the collocation method along with the operational matrix, we reduce the problem to a system of nonlinear algebraic equations, which is then solved using Newton–Raphson’s iterative procedure. The error estimate of the proposed method is analyzed, and numerical simulations are conducted to demonstrate its accuracy and efficiency. The obtained results are compared with existing approaches from the literature, highlighting the advantages of our method in terms of accuracy and computational performance.https://www.mdpi.com/2075-1680/14/3/185Müntz–Legendre waveletswavelet collocation methodfractional equationNewton’s iterative method |
| spellingShingle | Fatemeh Soleyman Iván Area Müntz–Legendre Wavelet Collocation Method for Solving Fractional Riccati Equation Axioms Müntz–Legendre wavelets wavelet collocation method fractional equation Newton’s iterative method |
| title | Müntz–Legendre Wavelet Collocation Method for Solving Fractional Riccati Equation |
| title_full | Müntz–Legendre Wavelet Collocation Method for Solving Fractional Riccati Equation |
| title_fullStr | Müntz–Legendre Wavelet Collocation Method for Solving Fractional Riccati Equation |
| title_full_unstemmed | Müntz–Legendre Wavelet Collocation Method for Solving Fractional Riccati Equation |
| title_short | Müntz–Legendre Wavelet Collocation Method for Solving Fractional Riccati Equation |
| title_sort | muntz legendre wavelet collocation method for solving fractional riccati equation |
| topic | Müntz–Legendre wavelets wavelet collocation method fractional equation Newton’s iterative method |
| url | https://www.mdpi.com/2075-1680/14/3/185 |
| work_keys_str_mv | AT fatemehsoleyman muntzlegendrewaveletcollocationmethodforsolvingfractionalriccatiequation AT ivanarea muntzlegendrewaveletcollocationmethodforsolvingfractionalriccatiequation |