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The aim of this paper is to construct and analyze exponential Runge-Kutta methods for the temporal discretization of a class of semilinear parabolic problems with arbitrary state-dependent delay. First, the well-posedness of the problem is…
A standard approach to solve ordinary differential equations, when they describe dynamical systems, is to adopt a Runge-Kutta or related scheme. Such schemes, however, are not applicable to the large class of equations which do not…
We apply Runge-Kutta methods to linear partial differential-algebraic equations of the form $Au_t(t,x) + B(u_{xx}(t,x)+ru_x(t,x))+Cu(t,x) = f(t,x)$, where $A,B,C\in\R^{n,n}$ and the matrix $A$ is singular. We prove that under certain…
We apply boundary integral equations for the first time to the two-dimensional scattering of time-harmonic waves from a smooth obstacle embedded in a continuously-graded unbounded medium. In the case we solve the square of the wavenumber…
This paper discusses the practical development of space-time boundary element methods for the wave equation in three spatial dimensions. The employed trial spaces stem from simplex meshes of the lateral boundary of the space-time cylinder.…
This paper proposes a frequency/time hybrid integral-equation method for the time dependent wave equation in two and three-dimensional spatial domains. Relying on Fourier Transformation in time, the method utilizes a fixed…
We introduce a general method for understanding the late time tail for solutions to wave equations on asymptotically flat spacetimes with odd space dimensions. In particular, for a large class of equations, we prove that the precise late…
The first partial boundary data complex geometrical optics based methods for electrical impedance tomography in three dimensions are developed, and tested, on simulated and experimental data. The methods provide good localization of targets…
Superquantiles have recently gained significant interest as a risk-aware metric for addressing fairness and distribution shifts in statistical learning and decision making problems. This paper introduces a fast, scalable and robust…
In this paper a technique is given to recover the classical order of the method when explicit exponential Runge-Kutta methods integrate reaction-diffusion problems. Although methods of high stiff order for problems with vanishing boundary…
We study the application of the generalized convolution quadrature (gCQ) based on Runge--Kutta methods to approximate the solution of an important class of sectorial problems. The gCQ generalizes Lubich's original convolution quadrature…
A linear evolving surface partial differential equation is first discretized in space by an arbitrary Lagrangian Eulerian (ALE) evolving surface finite element method, and then in time either by a Runge-Kutta method, or by a backward…
The exponential fitting technique uses information on the expected behaviour of the solution of a differential problem to define accurate and efficient numerical methods. In particular, exponentially fitted methods are very effective when…
In this paper the performance of a parallel iterated Runge-Kutta method is compared versus those of the serial fouth order Runge-Kutta and Dormand-Prince methods. It was found that, typically, the runtime for the parallel method is…
Efficient and accurate numerical simulation of 3D acoustic wave propagation in heterogeneous media plays an important role in the success of seismic full waveform inversion (FWI) problem. In this work, we employed the combined scheme and…
This paper develops a high-accuracy algorithm for time fractional wave problems, which employs a spectral method in the temporal discretization and a finite element method in the spatial discretization. Moreover, stability and convergence…
In quantum computing the decoherence time of the qubits determines the computation time available and this time is very limited when using current hardware. In this paper we minimize the execution time (the depth) for a class of circuits…
The boundary integral method is an efficient approach for solving time-harmonic acoustic obstacle scattering problems. The main computational task is the evaluation of an oscillatory boundary integral at each discretization point of the…
A general purpose, modular program package for the integration of large number of independent ordinary differential equation systems capable of using professional graphics cards is presented. The available numerical schemes are the explicit…
Exponential time differencing methods is a power tool for high-performance numerical simulation of computationally challenging problems in condensed matter physics, fluid dynamics, chemical and biological physics, where mathematical models…