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In this work, we present approaches to rigorously certify A- and A ( α )-stability in Runge-Kutta methods through the solution of convex feasibility problems defined by linear matrix inequalities. We adopt two approaches. The first is based on ...

• Sharpening algebraic conditions for A-stability of Runge-Kutta methods.
• Providing rigorous stability certificates for Runge-Kutta schemes.
• Certifying A- and A(a)-stability via convex feasibility SDP problems.

In this paper, a time-explicit Finite-Volume method is adopted to solve the 2-D shallow water equations on an unstructured triangular mesh, using a two-stage Runge-Kutta integrator and a monotone MUSCL model to achieve second-order accuracy in ...

• We expressed the shallow-water equations for a 2D area for numerical solution via parallel computation using MPI and OpenACC.
• Various parallel computing techniques are optimized to improve the code's performance.
• The single-GPU ...

A numerical search approach is used to design high-order diagonally implicit Runge-Kutta (DIRK) time stepping schemes equipped with embedded error estimators, some of which have identical diagonal elements (i.e., SDIRK) and explicit first stage (...

We present a high-order sharp treatment of immersed moving domain boundaries and material interfaces, and apply it to the advection-diffusion equation in two and three dimensions. The spatial discretization combines dimension-split finite ...

• Developed and analyzed novel sharp immersed method for PDEs with moving boundaries.
• The approach is compatible with a wide range of high-order time integration schemes.
• The moving boundary treatment achieves high order spatial/...

Spline Quasi-Interpolation (QI) of even degree 2R on general partitions is introduced, where derivative information up to order R ≥ 1 at the spline breakpoints is required and maximal convergence order can be proved. Relying on the B-spline basis ...

Aiming at the problem of trajectory tracking control for mobile robot nonlinear systems with non-repetitive uncertain parameters, we propose a novel neural network compensator-based robust iterative learning control (NNRILC) scheme to achieve ...

• A novel ILC scheme combining neural network compensator is designed to solve trajectory tracking problem.
• The Runge-Kutta algorithm is introduced to solve the state differential equation and the controller equation.
• A neural ...

Many low-Mach or all-Mach number codes are based on space discretizations which in combination with the first order explicit Euler method as time integration would lead to an unstable scheme. In this paper, we investigate how the choice of a ...

• All Mach and low Mach Riemannsolvers usable with suitable explicit time integration.
• Explicit Runge-Kutta methods suffer from unstable stage value.
• Linear Multistep Methods provide good alternatives.

Numerical errors are insidious, difficult to predict and inherent in different levels of critical systems design. Indeed, numerical algorithms generally constitute approximations of an ideal mathematical model, which itself constitutes an ...

Runge–Kutta embedded pairs of high algebraic order are frequently utilized when strict tolerances are required. When creating such pairings of orders nine and eight for use in double precision arithmetic, numerous conditions are often satisfied. ...

Recently, Paired Explicit Runge-Kutta (P-ERK) schemes were introduced to accelerate the solution of locally-stiff systems of equations. P-ERK schemes use different numbers of active stages based on local stiffness criteria, ...

• An embedded pair framework is given for Paired Explicit Runge-Kutta (P-ERK) schemes.

Runge–Kutta methods for the numerical solution of inhomogeneous linear initial value problems with constant coefficients are considered.

A general procedure to construct explicit s-stage RK methods with order s, for the ...

In this work, we present a modification of explicit Runge–Kutta temporal integration schemes that guarantees the preservation of any locally-defined quasiconvex set of bounds for the solution. These schemes operate on the basis of a bijective ...

In this article, a study has been carried out to further develop the Runge–Kutta (RK) algorithm, which has a current and robust mathematical structure, using the fitness distance balance (FDB) method, and to test it for induction machine control. ...

Pulmonary tuberculosis is caused by Mycobacterium tuberculosis (Mtb) which attacks the body's immune cells. A better understanding of the interactions of Mtb, macrophages, and T cells will help control tuberculosis. This interaction is represented ...

This note addresses the question of whether stage pseudo-pressures can be used to build high-accuracy instantaneous pressure estimates in the context of projection-based Navier-Stokes solvers. The construction of such estimates using ...

• Successful candidate strategy coupled with Runge-Kutta optimization (ScsRUN) is proposed.

The hydropower problems are non-linear and non-convex in nature; therefore, optimizing the operations of multi-hydropower plants in a multi-reservoir system is always challenging and complicated. In order to develop an appropriate ...

The ability to advance locally-stiff systems of equations in time depends on accurate and efficient temporal schemes. Recently, a new family of Paired Explicit Runge-Kutta (P-ERK) methods has been proposed. This approach allows ...

• We propose novel third-order Paired Explicit Runge-Kutta (P-ERK) schemes.
• These ...

In this work we consider a mixed precision approach to accelerate the implementation of multi-stage methods. We show that Runge–Kutta methods can be designed so that certain costly intermediate computations can be performed as a lower-precision ...

We introduce a class of high order accurate, semi-implicit Runge-Kutta schemes in the general setting of evolution equations that arise as gradient flow for a cost function, possibly with respect to an inner product that depends on the ...

• High-order, energy stable, semi-implicit schemes for general gradient flows.
• ...

In this paper we generate optimized Runge-Kutta stability polynomials for multidimensional discontinuous Galerkin methods recovered using the flux reconstruction approach. Results from linear stability analysis demonstrate that these stability ...