Kernel Based High Order “Explicit” Unconditionally Stable Scheme for Nonlinear Degenerate Advection-Diffusion Equations

A kernel based high order “explicit” unconditionally stable scheme for time dependent Hamilton–Jacobi equations

(2018) Andrew Christlieb et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A WENO-based Method of Lines Transpose approach for Vlasov simulations

(2016) Andrew Christlieb et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Method of Lines Transpose: High Order L-Stable ${\mathcal O}(N)$ Schemes for Parabolic Equations Using Successive Convolution

(2016) Matthew F. Causley et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Method of lines transpose: An implicit solution to the wave equation

(2014) Matthew Causley et al.   MATHEMATICS OF COMPUTATION

Higher Order A-Stable Schemes for the Wave Equation Using a Successive Convolution Approach

(2014) Matthew F. Causley et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

A high-order weighted essentially non-oscillatory (WENO) finite difference scheme for nonlinear degenerate parabolic equations

(2013) Rooholah Abedian et al.   COMPUTER PHYSICS COMMUNICATIONS

A Finite Volume Scheme for Nonlinear Degenerate Parabolic Equations

(2012) Marianne Bessemoulin-Chatard et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

High accurate NRK and MWENO scheme for nonlinear degenerate parabolic PDEs

(2011) Mojtaba Hajipour et al.   APPLIED MATHEMATICAL MODELLING

Fast integral equation methods for Rothe’s method applied to the isotropic heat equation

(2011) Mary Catherine A. Kropinski et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

Step Sizes for Strong Stability Preservation with Downwind-Biased Operators

(2011) David I. Ketcheson   SIAM JOURNAL ON NUMERICAL ANALYSIS

High Order Finite Difference WENO Schemes for Nonlinear Degenerate Parabolic Equations

(2011) Yuanyuan Liu et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

On the positivity of linear weights in WENO approximations

(2009) Yuan-yuan Liu et al.   Acta Mathematicae Applicatae Sinica-English Series

High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems

(2009) Chi-Wang Shu   SIAM REVIEW

An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws

(2008) Rafael Borges et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Numerical Simulation for Porous Medium Equation by Local Discontinuous Galerkin Finite Element Method

(2008) Qiang Zhang et al.   JOURNAL OF SCIENTIFIC COMPUTING

Krylov deferred correction accelerated method of lines transpose for parabolic problems

(2007) Jun Jia et al.   JOURNAL OF COMPUTATIONAL PHYSICS