8 papers
Theory and internal structure of ADER-DG method for partial differential equations
I. S. Popov
Highly accurate stability boundary values for the ADER-DG method are obtained for arbitrary degrees of basis polynomials. In the linear case, stability is violated precisely wh…
Improving the local solution of the DG predictor of the ADER-DG method for solving systems of ordinary differential equations and its applicability to systems of differential-algebraic equations
I. S. Popov
Improved local numerical solution for the ADER-DG numerical method with a local DG predictor for solving the initial value problem for a first-order ODE system is proposed. The imp…
Theory and internal structure of ADER-DG method for ordinary differential equations
I. S. Popov
Investigation of the approximation properties, convergence, and stability of the ADER-DG method for solving an ODE system is carried out. The ADER-DG method is - and -stable…
The effective use of BLAS interface for implementation of finite-element ADER-DG and finite-volume ADER-WENO methods
I. S. Popov
Numerical methods of the ADER family, in particular finite-element ADER-DG and finite-volume ADER-WENO methods, are among the most accurate numerical methods for solving quasilinea…
High order ADER-DG method with local DG predictor for solutions of differential-algebraic systems of equations
I. S. Popov
A numerical method ADER-DG with a local DG predictor for solving a DAE system has been developed, which was based on the formulation of ADER-DG methods using a local DG predictor f…
Arbitrary high order ADER-DG method with local DG predictor for solutions of initial value problems for systems of first-order ordinary differential equations
I. S. Popov
An adaptation of the arbitrary high order ADER-DG numerical method with local DG predictor for solving the IVP for a first-order non-linear ODE system is proposed. The proposed num…