Differential - Operator solutions for complex partial differential equations

Date

1998-07-10

Author

Celebi, O
Sengul, S

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

231
views

0
downloads

The solutions of complex partial differential equations of order four are obtained by using polynomial differential operators. A correspondence principle is also derived for the solutions of two different differential equations, imposing conditions on the coefficients.

Subject Keywords

Partial differential equation, Differential operator, Integral operator, Operator solution, Correspondence principle

URI

https://hdl.handle.net/11511/65196

Conference Name

Workshop on Recent Trends in Complex Methods for Partial Differential Equations

Collections

Department of Mathematics, Conference / Seminar

Suggestions

OpenMETU
Core

Differential quadrature solution of nonlinear Klein-Gordon and sine-Gordon equations Pekmen, B.; Tezer, Münevver (2012-08-01) Differential quadrature method (DQM) is proposed to solve the one-dimensional quadratic and cubic Klein-Gordon equations, and two-dimensional sine-Gordon equation. We apply DQM in space direction and also blockwise in time direction. Initial and derivative boundary conditions are also approximated by DQM. DQM provides one to obtain numerical results with very good accuracy using considerably small number of grid points. Numerical solutions are obtained by using Gauss-Chebyshev-Lobatto (GCL) grid points in s...
Least squares differential quadrature time integration scheme in the dual reciprocity boundary element method solution of convection-diffusion problems Bozkaya, Canan (2005-03-18) The least squares differential quadrature method (DQM) is used for solving the ordinary differential equations in time, obtained from the application of the dual reciprocity boundary element method (DRBEM) for the spatial partial derivatives in convection-diffusion type problems. The DRBEM enables us to use the fundamental solution of the Laplace equation which is easy to implement computationally. The time derivative and the convection terms are considered as the nonhomogeneity in the equation which are ap...
Differential equations with discontinuities and population dynamics Aruğaslan Çinçin, Duygu; Akhmet, Marat; Department of Mathematics (2009) In this thesis, both theoretical and application oriented results are obtained for differential equations with discontinuities of different types: impulsive differential equations, differential equations with piecewise constant argument of generalized type and differential equations with discontinuous right-hand sides. Several qualitative problems such as stability, Hopf bifurcation, center manifold reduction, permanence and persistence are addressed for these equations and also for Lotka-Volterra predator-...
Exact Solutions of Some Partial Differential Equations Using the Modified Differential Transform Method Cansu Kurt, Ümmügülsüm; Ozkan, Ozan (2018-03-01) In this paper, we present the modification of the differential transform method by using Laplace transform and Pade approximation to obtain closed form solutions of linear and nonlinear partial differential equations. Some illustrative examples are given to demonstrate the activeness of the proposed technique. The obtained results ensure that this modified method is capable of solving a large number of linear and nonlinear PDEs that have wide application in science and engineering. It solves the drawbacks i...
Invariant manifolds and Grobman-Hartman theorem for equations with degenerate operator at the derivative Karasözen, Bülent; Loginov, B (2003-01-01) Analog of Grobman-Hartman theorem about stable and unstable manifolds solutions for differential equations in Banach spaces with degenerate Fredholm operator at the derivative are proved. In contrast to usual evolution equation here central manifold arises even in the case of spectrum absence on the imaginary axis. Jordan chains tools and implicit operator theorem are used. The obtained results allow to develop center manifold methods for computation of bifurcation solution asymptotics and their stability i...

Citation Formats

O. Celebi and S. Sengul, “Differential - Operator solutions for complex partial differential equations,” METU, Ankara Turkey, 1998, vol. 6, p. 29, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/65196.