Related papers: Using a template engine as a computer algebra tool
Dynamical systems are ubiquitous in science and engineering as models of phenomena that evolve over time. Although complex dynamical systems tend to have important modular structure, conventional modeling approaches suppress this structure.…
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…
Automatic programming attempts to minimize human intervention in the generation of executable code, and has been a long-standing challenge in the software engineering community. To advance automatic programming, researchers are focusing on…
Automatic generation of software code from system design models remains an actively explored research area for the past several years. A number of tools are currently available to facilitate and automate the task of generating code from…
This work focuses on the development of a new class of high-order accurate methods for multirate time integration of systems of ordinary differential equations. The proposed methods are based on a specific subset of explicit one-step…
Explicit Runge-Kutta methods are classical and widespread techniques in the numerical solution of ordinary differential equations (ODEs). Considering partial differential equations, spatial semidiscretisations can be used to obtain systems…
Since time immemorial an old adage has always seemed to ring true: you cannot use a high-level productive programming language like Python or R for real-time control and embedded-systems programming, you must rewrite your program in C. We…
Benchmark datasets have a significant impact on accelerating research in programming language tasks. In this paper, we introduce CodeXGLUE, a benchmark dataset to foster machine learning research for program understanding and generation.…
We introduce {\tt JuliBootS}, a package for numerical conformal bootstrap computations coded in {\tt Julia}. The centre-piece of {\tt JuliBootS} is an implementation of Dantzig's simplex method capable of handling arbitrary precision linear…
We demonstrate the effectiveness of a novel scheme for numerically solving linear differential equations whose solutions exhibit extreme oscillation. We take a standard Runge-Kutta approach, but replace the Taylor expansion formula with a…
The task of integrating a large number of independent ODE systems arises in various scientific and engineering areas. For nonstiff systems, common explicit integration algorithms can be used on GPUs, where individual GPU threads…
A critical step in developing circuits for quantum simulation is to synthesize a desired unitary operator using the circuit building blocks. Studying unitaries and their generators from the Lie algebraic perspective has given rise to…
Semi-Lagrangian methods are numerical methods designed to find approximate solutions to particular time-dependent partial differential equations (PDEs) that describe the advection process. We propose semi-Lagrangian one-step methods for…
This paper presents a novel approach to automatically solving arithmetic word problems. This is the first algorithmic approach that can handle arithmetic problems with multiple steps and operations, without depending on additional…
The cubic spline interpolation method, the Runge--Kutta method, and the Newton-Raphson method are extended to dual versions (developed in the context of dual numbers). This extension allows the calculation of the derivatives of complicated…
Generating high-performance code for diverse hardware and application domains is challenging. Functional array programming languages with patterns like map and reduce have been successfully combined with term rewriting to define and explore…
It is becoming increasingly clear that, if a useful device for quantum computation will ever be built, it will be embodied by a classical computing machine with control over a truly quantum subsystem, this apparatus performing a mixture of…
Stable computational algorithms for the approximate solution of the Cauchy problem for nonstationary problems are based on implicit time approximations. Computational costs for boundary value problems for systems of coupled multidimensional…
We propose an implementation of symplectic implicit Runge-Kutta schemes for highly accurate numerical integration of non-stiff Hamiltonian systems based on fixed point iteration. Provided that the computations are done in a given floating…
With the recent proliferation of open-source packages for computing, power system differential-algebraic equation (DAE) modeling and simulation are being revisited to reduce the programming efforts. Existing open-source tools require manual…