RESOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS BY THE MOLLIFICATION METHOD

Authors

Paulina Monserrate Alonzo Dumes Universidad Técnica de Manabí, Instituto de Posgrado, Portoviejo, Ecuador. https://orcid.org/0000-0002-6941-0521
Raúl Manzanilla Morillo Universidad Yachay Tech, Escuela de Ciencias Matemáticas y Computacionales, Urcuquí, Ecuador. https://orcid.org/0000-0002-8456-0333
Richard A. Rosales Rangel Universidad de Los Andes, Facultad de Ingeniería, Departamento de Cálculo, Mérida, Venezuela. https://orcid.org/0000-0002-6729-6120

DOI:

https://doi.org/10.33936/revbasdelaciencia.v8i3.6955

Keywords:

Finite differences, bubble function, gauss mollification.

Abstract

The Gauss function has been used in the mollification method to solve problems with solution have fast changes on the domain. This method use the function’s convolution like a tool for the estabilization of the results. It is propose polinomial functions or bubble functions like kernel of the molification to solve boundary values problems embebed in the ordinary differential equations. According to the results obtained, this method is capable of reducing the oscillations that appear when solving convection-diffusion problems with finite differences, allowing the use of polynomial kernels to obtain stable
and precise results.

Downloads

Download data is not yet available.

References

Acosta, C. D. y Mejıa, C. E. [Carlos E]. (2008). Stabilization of explicit methods for convection diffusion equations by discrete mollification. Computers & Mathematics with Applica- tions, 55 (3), 368-380.

Ambardar, A. (2002). Procesamiento de sen˜ales analogicas y digitales. Gerald, C. y Wheatley, P. (2000). Analisis Num´erico con Aplicaciones.

Guo, S. J. (1982). On the mollifier approximation for solutions of stochastic differential equa- tions. Journal of Mathematics of Kyoto University, 22 (2), 243-254.

Marechal, P., Lee, W. S. T. y Triki, F. (2021). A mollifier approach to regularize a Cauchy problem for the inhomogeneous Helmholtz equation. arXiv preprint arXiv:2105.02665.

Medina Olivera, V. J. (2018). Desarrollo de un Sistema Automatizado Basado en Procesamiento

Digital de Imagenes para mejorar el control de Videovigilancia en empresas de Trujillo. Mejıa, C. E. [C E] y Murio, D. A. [D A]. (1996). Numerical solution of generalized IHCP by

discrete mollification. Computers & Mathematics with Applications, 32 (2), 33-50.

Mejıa, C. E. [Carlos E]. (2007). Sobre el m´etodo de molificacion. Trabajo presentado como requisito parcial para promocion a profesor titular, Medellın, Universidad Nacional de Colombia.

Murio, D. A. [Diego A]. (1993). The mollification method and the numerical solution of ill-posed problems. John Wiley & Sons.

Nedeljkov, M. y Oberguggenberger, M. (2012). Ordinary differential equations with delta fun- ction terms. Publications de lI´nstitut Mathematique, 91 (105), 125-135.

Rosales, R. y Dıez, P. (2016). Un estimador de error residual semiexplıcito en cantidades de inter´es para un problema mec´anico lineal. Revista Internacional de M´etodos Num´ericos para C´alculo y Disen˜o en Ingenierıa, 32 (4), 212-220.

Smith, S. (2013). Digital signal processing: a practical guide for engineers and scientists. Else- vier.

Smith, S. W. y col. (1997). The scientist and engineer’s guide to digital signal processing.