Eficiencia de la Iteración de Newton de Orden 3, en la Solución Numérica por el Método de Disparo
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Alex Youn Aro Huanacuni
Oscar Santander Mamani
Resumen
El método de disparo es una técnica iterativa que usa velocidad de disparo para obtener una solución óptima. El propósito de la investigación es verificar la eficacia de las iteraciones de Newton de orden 3 adaptadas y acopladas a RK4, en el método disparo. Se realizó un experimento numérico con ejemplos mediante el método de disparo en las ecuaciones diferenciales ordinarias no lineal de orden 2, y se obtuvo velocidades de disparo y errores en cada iteración. Los resultados obtenidos sobre velocidades finales fueron satisfactorios con las iteraciones NW, NWO3-1, NWO3-2 y NWO3-3 aplicadas al método de disparo y de los cuales, NWO3-2 y NWO3-3 tienen alta precisión en los experimentos realizados.
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Ahsan, M., & Farrukh, S. (2013). A new type of shoo- ting method for nonlinear boundary value problems. Alexandria Engineering Journal, 52(4), 801–805. https://doi.org/10.1016/j.aej.2013.07.001
Attili, B., & Syam, M. (2008). Efficient shooting method for solving two point boundary value problems. Chaos, Solitons and Fractals, 35(5), 895–903. https://doi.org/10.1016/j.chaos.2006.05.094
Bailey, P., & Shampine, L. (1968). On shooting methods for two-point boundary value problems. Journal of Mathematical Analysis and Applications, 23(2), 235–249. https://doi.org/10.1016/0022-247X(68)90064-4
Burden, R., Faires, J., & Burden, A. (2017). Análisis Numérico (10th ed.). Cengage Learning.
Butcher, J. (1996). History of Runge-Kutta methods. Appllied Numerical Mathematics, 20(3), 247–260. https://doi.org/10.1016/0168-9274(95)00108-5
Darvishi, M., & Barati, A. (2007). A third-order Newton- type method to solve systems of nonlinear equations. Applied Mathematics and Computation, 187(2), 630–635. https://doi.org/10.1016/j.amc.2006.08.080
Filipov, S., Gospodinov, I., & Faragó, I. (2017). Shooting- projection method for two-point boundary value problems. Applied Mathematics Letters, 72, 10–15. https://doi.org/10.1016/j.aml.2017.04.002
Granas, A., Guenther, R., & Lee, J. (1979). The Shooting Method for the Numerical Solution of a Class of Nonlinear Boundary Value Problems. SIAM Journal on Numerical Analysis, 16(5), 828–836. https://doi.org/10.1137/0716062
Ha, S. N. (2001). A nonlinear shooting method for two-point boundary value problems. Computers and Mathematics with Applications, 42(10–11), 1411–1420. https://doi.org/10.1016/S0898-1221(01)00250-4
Keller, H. B. (2018). Numerical Methods for Two-Point Boundary- Value Problems. Dover Publications.
Kutta, W. (1901). Beitrag zur näherungsweisen Integration otaler Differentialgleichungen. Zeit. Math. Phys., 46, 435–453.
Liu, C. (2006). The Lie-group shooting method for non- linear two-point boundary value problems exhibiting multiple solutions. CMES - Computer Modeling in Engineering and Sciences, 13(2), 149–163. https://doi.org/10.3970/cmes.2006.013.149
Magreñán Ruiz, Á., & Argyros, I. (2014). Two-step Newton methods. Journal of Complexity, 30(4), 533–553. https://doi.org/10.1016/j.jco.2013.10.002
Mataušek, M. (1974). Direct shooting method, linearization, and nonlinear algebraic equations. Journal of Optimization Theory and Applications, 14(2), 199–212. https://doi.org/10.1007/BF00932940
NumPy. (2022). NumPy User Guide v1.3. https://numpy.org/doc/1.23/numpy-ref.pdf
Osborne, M. (1969). On shooting methods for boundary value problems. Journal of Mathematical Analysis and Applications, 27(2), 417–433. https://doi.org/10.1016/0022-247X(69)90059-6
Schrader, K. (1969). Existence theorems for second order boundary value problems. Journal of Differential Equations, 5(3), 572–584. https://doi.org/10.1016/0022-0396(69)90094-1
SymPy. (2022). SymPy Documentation. https://github.com/sympy/sympy/releases
Weerakoon, S., & Fernando, T. (2000). A variant of Newton’s method with accelerated third-order convergence. Applied Mathematics Letters, 13(8), 87–93. https://doi.org/10.1016/S0893-9659(00)00100-2
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