# Numerical Methods for Partial Differential Equations

Numerical Methods for Partial Differential Equations > 26 > 2 > 274 - 289

*N*‐carrier system with heat sources and Neumann boundary conditions, which extends the concept of the well‐known parabolic two‐step model for microheat transfer. By using the matrix analysis, the compact finite difference numerical scheme is shown to be unconditionally...

Numerical Methods for Partial Differential Equations > 26 > 5 > 1079 - 1098

*N*‐carrier system with Neumann boundary conditions, which extends the concept of the well‐known parabolic two‐step model for micro heat transfer. To solve numerically the complex system, we first reduce 3D equations in the model to a succession of 1D equations by using the local one‐dimensional (LOD) method. The obtained 1D equations are...

Numerical Methods for Partial Differential Equations > 27 > 2 > 436 - 446

Numerical Methods for Partial Differential Equations > 27 > 3 > 507 - 528

Numerical Methods for Partial Differential Equations > 27 > 3 > 554 - 580

Numerical Methods for Partial Differential Equations > 27 > 5 > 1179 - 1200

Numerical Methods for Partial Differential Equations > 27 > 6 > 1561 - 1583

Numerical Methods for Partial Differential Equations > 28 > 2 > 402 - 424

Numerical Methods for Partial Differential Equations > 28 > 6 > 2010 - 2020

*N*‐carrier system with Neumann boundary conditions. This model extends the concept of the well‐known parabolic two‐step model for microheat transfer to the energy exchanges in a generalized

*N*‐carrier system with heat sources. The energy norm stability and error estimate of the LDG method...

Numerical Methods for Partial Differential Equations > 28 > 6 > 1944 - 1965

Numerical Methods for Partial Differential Equations > 28 > 6 > 1893 - 1915

Numerical Methods for Partial Differential Equations > 29 > 1 > 186 - 205

Numerical Methods for Partial Differential Equations > 29 > 1 > 206 - 225

Numerical Methods for Partial Differential Equations > 29 > 3 > 1031 - 1042

*v*

_{tt}=

*v*

_{xx}(0 <

*x*< 1,

*t*> 0) and its finite difference analogue with nonuniform time meshes. We are going to discuss the stability for such schemes. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013

Numerical Methods for Partial Differential Equations > 29 > 5 > 1459 - 1486

*O*(τ

^{2}+

*h*

^{4}) for interior mesh point approximation...

Numerical Methods for Partial Differential Equations > 29 > 5 > 1441 - 1458

Numerical Methods for Partial Differential Equations > 29 > 6 > 1912 - 1945

Numerical Methods for Partial Differential Equations > 31 > 3 > 706 - 722

_{∞}convergence of the finite difference scheme are proved by the energy method. Numerical...

Numerical Methods for Partial Differential Equations > 31 > 6 > 1742 - 1768

Numerical Methods for Partial Differential Equations > 32 > 2 > 591 - 615