Cubic B-Spline method for the solution of the quadratic Riccati differential equation

Osama Ala'yed; Belal Batiha; Diala Alghazo; Firas Ghanim; Osama Ala'yed; Belal Batiha; Diala Alghazo; Firas Ghanim

doi:10.3934/math.2023483

AIMS Mathematics

2023, Volume 8, Issue 4: 9576-9584. doi: 10.3934/math.2023483

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Cubic B-Spline method for the solution of the quadratic Riccati differential equation

1.
Department of Mathematics, Jadara University, Irbid 21110, Jordan
2.
Department of Mathematics, University of Sharjah, Sharjah, United Arab Emirates

Received: 07 October 2022 Revised: 25 December 2022 Accepted: 27 January 2023 Published: 20 February 2023
MSC : 65D07, 65G99, 65L05

The quadratic Riccati equations are first-order nonlinear differential equations with numerous applications in various applied science and engineering areas. Therefore, several numerical approaches have been derived to find their numerical solutions. This paper provided the approximate solution of the quadratic Riccati equation via the cubic b-spline method. The convergence analysis of the method is discussed. The efficiency and applicability of the proposed approach are verified through three numerical test problems. The obtained results are in good settlement with the exact solutions. Moreover, the numerical results indicate that the proposed cubic b-spline method attains a superior performance compared with some existing methods.
- Cubic b-spline method,
- nonlinear equations,
- numerical analysis,
- Riccati differential equation,
- first-order differential equations
Citation: Osama Ala'yed, Belal Batiha, Diala Alghazo, Firas Ghanim. Cubic B-Spline method for the solution of the quadratic Riccati differential equation[J]. AIMS Mathematics, 2023, 8(4): 9576-9584. doi: 10.3934/math.2023483

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Abstract

The quadratic Riccati equations are first-order nonlinear differential equations with numerous applications in various applied science and engineering areas. Therefore, several numerical approaches have been derived to find their numerical solutions. This paper provided the approximate solution of the quadratic Riccati equation via the cubic b-spline method. The convergence analysis of the method is discussed. The efficiency and applicability of the proposed approach are verified through three numerical test problems. The obtained results are in good settlement with the exact solutions. Moreover, the numerical results indicate that the proposed cubic b-spline method attains a superior performance compared with some existing methods.

References

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