A matched Hermite-Taylor matrix method to solve the combined partial integro-differential equations having nonlinearity
- PDF / 1,236,973 Bytes
- 16 Pages / 439.37 x 666.142 pts Page_size
- 32 Downloads / 152 Views
A matched Hermite-Taylor matrix method to solve the combined partial integro-differential equations having nonlinearity and delay terms Elif Yalçın1
· Ömür Kıvanç Kürkçü2
· Mehmet Sezer1
Received: 24 January 2020 / Revised: 29 August 2020 / Accepted: 14 September 2020 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2020
Abstract In this study, a matched numerical method based on Hermite and Taylor matrix-collocation techniques is developed to obtain the numerical solutions of a combination of the partial integro-differential equations (PIDEs) under Dirichlet boundary conditions, which involve the nonlinearity, delay and Volterra integral terms. These type equations govern wide variety applications in physical sense. The present method easily constitutes the matrix relations of the linear and nonlinear terms in a considered PIDE, using the eligibilities of the Hermite and Taylor polynomials. It thus directly produces a polynomial solution by eliminating a matrix system of nonlinear algebraic functions gathered from the matrix relations. Besides, the validity and precision of the method are tested on stiff examples by fulfilling several error computations. One can state that the method is fast, validate and productive according to the numerical and graphical results Keywords Hermite and Taylor polynomials · Matrix method · Delay · Nonlinearity · Collocation points Mathematics Subject Classification 45K05 · 65N35
1 Introduction In recent years, a great deal of necessity for modelling real world phenomena has drastically increased with the developments of the phenomena occurring in science and technology. In doing so, mathematical tools are employed to model the physical behavior of these phenomena. One of them is partial integro-differential equations (PIDEs) that combine the partial differential equation with the integral equation by involving their many subclasses. This
Communicated by Hui Liang.
B
Ömür Kıvanç Kürkçü [email protected]
1
Department of Mathematics, Manisa Celal Bayar University, Manisa 45140, Turkey
2
Department of Engineering Basic Sciences, Konya Technical University, Konya 42250, Turkey 0123456789().: V,-vol
123
280
Page 2 of 16
E. Yalçın et al.
combination gives rise to directly govern specific physical phenomena arising widely in mathematics, physics, biological processes, engineering, mechanics, radiation propagation, transport models, geophysics, heat conductors and biofluids flow in fractured biomaterials (Gürbüz and Sezer 2017; Appell et al. 2000; Aziz and Khan 2018; Barbashin 1957; Bloom 1981; Grasselli et al. 1990; Habetler and Schiffman 1970; Miller 1978; Zadeh 2011). As physical phenomena are exposed to external evolution, such as technological innovation, scientific developments and real world applications, scopes of PIDEs are increased due to the involvement of nonlinear and delay forces in their structures. For more specification, convection-reaction diffusion systems can be processed with nonlinear forces and also a delay force can determin
Data Loading...
