## Related Articles

- Inverse problem for an equation of mixed type with the Lavrent'ev-Bitsadze operator and with a nonlocal boundary condition. Yunusova, G. // Differential Equations;Mar2013, Vol. 49 Issue 3, p395
For an equation of the mixed elliptic-hyperbolic type, we study the inverse problem with a nonlocal condition relating the derivatives of the solution on the elliptic and hyperbolic parts of the boundary. We prove a uniqueness criterion and construct the solution in the form of a Fourier series.

- Error estimates for projection-difference schemes for degenerate nonstationary equations. Lyashko, A. D.; Fedotov, E. M. // Differential Equations;Jul2006, Vol. 42 Issue 7, p1013
The article presents convergence theorems and error estimates for the solution of degenerate parabolic and hyperbolic equations, wherein the error estimate is derived by reducing the estimate to the difference between the solution of the problem and the orthogonal projection of the elliptic...

- Flux-splitting schemes for parabolic equations with mixed derivatives. Vabishchevich, P. // Computational Mathematics & Mathematical Physics;Aug2013, Vol. 53 Issue 8, p1139
Difference schemes of required quality are often difficult to construct as applied to boundary value problems for parabolic equations with mixed derivatives. Specifically, difficulties arise in the design of monotone difference schemes and unconditionally stable locally one-dimensional splitting...

- Inverse Neumann problem for an equation of elliptic type. Ashyralyyev, Charyyar // AIP Conference Proceedings;2014, Vol. 1611, p46
Inverse problem for an elliptic differential equation with Neumann conditions is considered. Stability and coercive stability estimates for the solution of inverse problem with the overdetermination are obtained. The first and second order of accuracy difference schemes are presented. Stability...

- RATE OF CONVERGENCE OF FINITE-DIFFERENCE APPROXIMATIONS FOR DEGENERATE LINEAR PARABOLIC EQUATIONS WITH CÂ¹ AND CÂ² COEFFICIENTS. Hongjie Dong; Krylov, Nicolai V. // Electronic Journal of Differential Equations;2005, Vol. 2005, p1
We consider degenerate parabolic and elliptic equations of second order with CÂ¹ and CÂ² coefficients. Error bounds for certain types of finite-difference schemes are obtained.

- Ð˜Ð¡Ð¡Ð›Ð•Ð”ÐžÐ’ÐÐÐ˜Ð• Ð”Ð’Ð£Ð¥Ð¡Ð•Ð¢ÐžÐ§ÐÐžÐ“Ðž ÐœÐ•Ð¢ÐžÐ”Ð ÐŸÐžÐ’Ð«Ð¨Ð•ÐÐÐžÐ™ Ð¢ÐžÐ§ÐÐžÐ¡Ð¢Ð˜ Ð”Ð›Ð¯ ÐÐ›Ð›Ð˜ÐŸÐ¢Ð˜Ð§Ð•Ð¡ÐšÐžÐ“Ðž Ð£Ð ÐÐ’ÐÐ•ÐÐ˜Ð¯ Ð Ð•ÐÐšÐ¦Ð˜Ð˜â€“Ð”Ð˜Ð¤Ð¤Ð£Ð—Ð˜Ð˜ Ð¡ ÐŸÐžÐ“Ð ÐÐÐ˜Ð§ÐÐ«ÐœÐ˜ Ð¡Ð›ÐžÐ¯ÐœÐ˜. Тиховская, С. В. // Proceedings of Kazan University. Physics & Mathematics Series / ;2015, Vol. 157 Issue 1, p60
A two-grid method for the elliptic equation with a small parameter Îµ multiplying the highest derivative is investigated. The Îµ-uniformly convergent difference scheme on the Shishkin mesh is considered. To resolve the difference scheme, a two-grid method with Îµ-uniform interpolation...

- An Approximation of Three-Dimensional Semiconductor Devices by Mixed Finite Element Method and Characteristics-Mixed Finite Element Method. Yang, Qing; Yuan, Yirang // Numerical Mathematics: Theory, Methods & Applications;Aug2015, Vol. 8 Issue 3, p356
The mathematical model for semiconductor devices in three space dimensions are numerically discretized. The system consists of three quasi-linear partial differential equations about three physical variables: the electrostatic potential, the electron concentration and the hole concentration. We...

- A 3D Finite-Difference BiCG Iterative Solver with the Fourier-Jacobi Preconditioner for the Anisotropic EIT/EEG Forward Problem. Turovets, Sergei; Volkov, Vasily; Zherdetsky, Aleksej; Prakonina, Alena; Malony, Allen D. // Computational & Mathematical Methods in Medicine;Jan2014, p1
The Electrical Impedance Tomography (EIT) and electroencephalography (EEG) forward problems in anisotropic inhomogeneous media like the human head belongs to the class of the three-dimensional boundary value problems for elliptic equations with mixed derivatives. We introduce and explore the...

- Multilevel correction adaptive finite element method for semilinear elliptic equation. Lin, Qun; Xie, Hehu; Xu, Fei // Applications of Mathematics;Oct2015, Vol. 60 Issue 5, p527
A type of adaptive finite element method is presented for semilinear elliptic problems based on multilevel correction scheme. The main idea of the method is to transform the semilinear elliptic equation into a sequence of linearized boundary value problems on the adaptive partitions and some...

- Equilibrium configurations of plasma in the approximation of two-fluid magnetohydrodynamics with electron inertia taken into account. Gavrikov, M.; Savelyev, V. // Journal of Mathematical Sciences;Nov2009, Vol. 163 Issue 1, p1
A single-fluid version of the equations of two-fluid magnetohydrodynamics is obtained. This paper is concerned with the following topics: derivation of the energy conservation law; proof of degenerate ellipticity of the the generalized AmpÃ¨reâ€™s law; passage to the limit to the...