scholarly journals A splitting method for a backward parabolic equation with time-dependent coefficients

2013 ◽  
Vol 65 (1) ◽  
pp. 17-28 ◽  
Author(s):  
Nguyen Thi Ngoc Oanh
Keyword(s):  
Parabolic Equation ◽  
Splitting Method ◽  
Time Dependent

scholarly journals Integrating Semilinear Wave Problems with Time-Dependent Boundary Values Using Arbitrarily High-Order Splitting Methods

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1113
Author(s):  
Isaías Alonso-Mallo ◽  
Ana M. Portillo
Keyword(s):  
Numerical Experiments ◽  
Splitting Method ◽  
Method Of Lines ◽  
Time Integration ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
High Order ◽  
Time Dependent ◽  
Boundary Values ◽  
Lipschitz Continuous

The initial boundary-value problem associated to a semilinear wave equation with time-dependent boundary values was approximated by using the method of lines. Time integration is achieved by means of an explicit time method obtained from an arbitrarily high-order splitting scheme. We propose a technique to incorporate the boundary values that is more accurate than the one obtained in the standard way, which is clearly seen in the numerical experiments. We prove the consistency and convergence, with the same order of the splitting method, of the full discretization carried out with this technique. Although we performed mathematical analysis under the hypothesis that the source term was Lipschitz-continuous, numerical experiments show that this technique works in more general cases.

scholarly journals Doubly Degenerate Parabolic Equation with Time-Dependent Gradient Source and Initial Data Measures

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Lihua Deng ◽  
Xianguang Shang
Keyword(s):  
Parabolic Equation ◽  
Initial Data ◽  
Degenerate Parabolic Equation ◽  
A Priori Estimates ◽  
A Priori ◽  
Local Existence ◽  
Time Dependent ◽  
Priori Estimates ◽  
The Cauchy Problem ◽  
Degenerate Parabolic

This paper is devoted to the Cauchy problem for a class of doubly degenerate parabolic equation with time-dependent gradient source, where the initial data are Radon measures. Using the delicate a priori estimates, we first establish two local existence results. Furthermore, we show that the existence of solutions is optimal in the class considered here.

scholarly journals A high order splitting method for time-dependent domains

2008 ◽  
Vol 197 (51-52) ◽  
pp. 4763-4773 ◽  
Author(s):  
Tormod Bjøntegaard ◽  
Einar M. Rønquist
Keyword(s):  
Splitting Method ◽  
High Order ◽  
Time Dependent

A Numerical Study of Quantum Decoherence

2012 ◽  
Vol 12 (1) ◽  
pp. 85-108 ◽  
Author(s):  
Riccardo Adami ◽  
Claudia Negulescu
Keyword(s):  
Density Matrix ◽  
Particle Density ◽  
Numerical Study ◽  
Heavy Particle ◽  
Splitting Method ◽  
Time Dependent ◽  
Quantum Decoherence ◽  
Approximation Formula ◽  
Time Splitting ◽  
Decoherence Effect

AbstractThe present paper provides a numerical investigation of the decoherence effect induced on a quantum heavy particle by the scattering with a light one. The time dependent two-particle Schrödinger equation is solved by means of a time-splitting method. The damping undergone by the non-diagonal terms of the heavy particle density matrix is estimated numerically as well as the error in the Joos-Zeh approximation formula.

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