3,270 Citations
A modified splitting method for the cubic nonlinear Schrödinger equation
- MathematicsArXiv
- 2022
. As a classical time-stepping method, it is well-known that the Strang splitting method reaches the first-order accuracy by losing two spatial derivatives. In this paper, we propose a modified…
A unified formulation of splitting-based implicit time integration schemes
- Computer ScienceJ. Comput. Phys.
- 2022
Higher Order Auxiliary Field Quantum Monte Carlo Methods
- PhysicsJournal of Physics: Conference Series
- 2022
The auxiliary field quantum Monte Carlo (AFQMC) method has been a workhorse in the field of strongly correlated electrons for a long time and has found its most recent implementation in the ALF…
Stability and Error Estimate of the Operator Splitting Method for the Phase Field Crystal Equation
- Materials ScienceJournal of Scientific Computing
- 2021
In this paper, we propose a second-order fast explicit operator splitting method for the phase field crystal equation. The basic idea lied in our method is to split the original problem into linear…
Numerical Investigation of Modified Fornberg Whitham Equation
- MathematicsMathematical Sciences and Applications E-Notes
- 2021
The aim of this study is to obtain numerical solutions of the modified Fornberg Whitham equation via collocation finite element method combined with operator splitting method. The splitting method is…
Detailed Population Balance Modelling of Titanium Dioxide Nanoparticle Synthesis
- Chemistry
- 2020
Venator National Research Foundation (NRF), Prime Minister’s Office, Singapore under its Campus for Research Excellence and Technological Enterprise (CREATE) programme.
Numerical Solution of Burger's Type Equation Using Finite Element Collocation method with Strang Splitting
- PhysicsMathematical Sciences and Applications E-Notes
- 2020
The nonlinear Burgers equation, which has a convection term, a viscosity term and a time dependent term in its structure, has been splitted according to the time term and then has been solved by…
Computational Simulation and Modeling of Heat Release Effects on Turbulence in Turbulent Reacting Flow
- Engineering, Physics
- 2018
This dissertation concerns the analysis and modeling of turbulence dynamics in turbulent combustion. In certain regimes of turbulent combustion, dilatation (volumetric expansion) induced by chemical…
Operator Splitting Solution of Equal Width Wave Equation Based on the Lie-Trotter and Strang Splitting Methods
- Physics
- 2018
In the present work, we have applied four different algoritms based on the Lie-Trotter and Strang splitting methods to obtain numerical solution of Equal Width (EW) equation. For this purpose, EW…
Operator splitting for numerical solution of the modified Burgers' equation using finite element method
- MathematicsNumerical Methods for Partial Differential Equations
- 2018
The aim of this study is to obtain numerical behavior of a one‐dimensional modified Burgers' equation using cubic B‐spline collocation finite element method after splitting the equation with Strang…
References
SHOWING 1-10 OF 13 REFERENCES
Numerical methods in multidimensional shocked flows
- Physics
- 1964
Numerical methods are described for the calculation of two-dimensional time-dependent in viscid flows that contain shocks. Methods are employed which do not consider the shock as in interior moving…
RICHTMYER, A survey of difference methods for nonsteady fluid dynamics, Tech
- Note 63-2,
- 1962
CROWLEY, Second-order numerical advection
- J. Comp. Phys.,
- 1967
WENDROFF, Difference schemes for hyperbolic equations with high order of accuracy, Comm
- Pure Appl. Math.,
- 1964
WENDROFF, Systems of conservation laws, Comm
- Pure Appl. Math.,
- 1960
A Runge-Kutta for all Seasons
- Computer Science
- 1967
By analyzing the trends over N steps at once, stimates of the accuracy can be derived which compare in reliability with those for classic predictor-corrector methods.
Systems of conservation laws
- Mathematics
- 1960
Abstract : In this paper a wide class of difference equations is described for approximating discontinuous time dependent solutions, with prescribed initial data, of hyperbolic systems of nonlinear…