Related papers: Using a template engine as a computer algebra tool
A space-time fully adaptive multiresolution method for evolutionary non-linear partial differential equations is presented introducing an improved local time-stepping method. The space discretisation is based on classical finite volumes,…
Differential flatness enables efficient planning and control for underactuated robotic systems, but we lack a systematic and practical means of identifying a flat output (or determining whether one exists) for an arbitrary robotic system.…
Approximating partial differential equations for extensive industrial and scientific applications requires leveraging the power of modern high-performance computing. In large-scale parallel computations, the geometrical discretisation…
Developers often search for relevant code examples on the web for their programming tasks. Unfortunately, they face two major problems. First, the search is impaired due to a lexical gap between their query (task description) and the…
Modernizing legacy enterprise systems often involves translating PL/I programs into modern languages such as Java. This task becomes significantly more complex when PL/I macro procedures are involved. The PL/I macro procedures are…
Existing methods fail to effectively steer Large Language Models (LLMs) between textual reasoning and code generation, leaving symbolic computing capabilities underutilized. We introduce CodeSteer, an effective method for guiding LLM…
This article discusses a new technique to automatically generate test cases for object oriented programs. At the state of the art, the problem of generating adequate sets of complete test cases has not been satisfactorily solved yet. There…
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…
We introduce the third major version of Metatheory.jl, a Julia library for general-purpose metaprogramming and symbolic computation. Metatheory.jl provides a flexible and performant implementation of e-graphs and Equality Saturation (EqSat)…
Additive Runge-Kutta methods designed for preserving highly accurate solutions in mixed-precision computation were proposed and analyzed in 4. These specially designed methods use reduced precision for the implicit computations and full…
Symbolic execution helps check programs by exploring different paths based on symbolic inputs. Tools like KLEE are commonly used because they can automatically detect bugs and create test cases. But one of KLEE's biggest issues is how slow…
We present a generalisation of King's symbolic execution technique called compact symbolic execution. It is based on a concept of templates: a template is a declarative parametric description of such a program part, generating paths in…
The purpose of this research is to propose a new approach named the shifted Bessel Tau (SBT) method for solving higher-order ordinary differential equations (ODE). The operational matrices of derivative, integral and product of shifted…
This paper concerns the numerical procedure for solving hybrid optimal control problems with sliding modes. The proposed procedure has several features which distinguishes it from the other procedures for the problem. First of all a sliding…
We present Ungar, an open-source library to aid the implementation of high-dimensional optimal control problems (OCPs). We adopt modern template metaprogramming techniques to enable the compile-time modeling of complex systems while…
Background: Component-based modeling language Modelica (OpenModelica is open source implementation) is used for the numerical simulation of complex processes of different nature represented by ODE system. However, in OpenModelica standard…
Algorithms are presented for the tanh- and sech-methods, which lead to closed-form solutions of nonlinear ordinary and partial differential equations (ODEs and PDEs). New algorithms are given to find exact polynomial solutions of ODEs and…
In this paper we define an efficient implementation of Runge-Kutta methods of Radau IIA type, which are commonly used when solving stiff ODE-IVPs problems. The proposed implementation relies on an alternative low-rank formulation of the…
We develop error-control based time integration algorithms for compressible fluid dynamics (CFD) applications and show that they are efficient and robust in both the accuracy-limited and stability-limited regime. Focusing on discontinuous…
This paper presents our approach to use refactoring techniques together with code generation. Refactoring is particularly useful if not only the generated classes but also the generator itself can be adapted in an automatic fashion. We have…