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The Poisson-Nernst-Planck (PNP) equations are one of the most effective model for describing electrostatic interactions and diffusion processes in ion solution systems, and have been widely used in the numerical simulations of biological…

Numerical Analysis · Mathematics 2023-12-19 Yang Liu , Shi Shu , Ying Yang

The integration of Fourier transform and deep learning opens new avenues for time series forecasting. We reconsider the Fourier transform from a basis functions perspective. Specifically, the real and imaginary parts of the frequency…

Machine Learning · Computer Science 2025-08-05 Runze Yang , Longbing Cao , Xin You , Kun Fang , Jianxun Li , Jie Yang

Engineered systems naturally experience large disturbances that can disrupt desired operation because the system may fail to recover to a stable equilibrium point. It is valuable to determine the mechanism of instability when the system is…

Systems and Control · Electrical Eng. & Systems 2025-03-18 Jinghan Wang , Michael W. Fisher

The context of this paper is the simulation of parameter-dependent partial differential equations (PDEs). When the aim is to solve such PDEs for a large number of parameter values, Reduced Basis Methods (RBM) are often used to reduce…

Numerical Analysis · Mathematics 2021-04-07 Elise Grosjean , Yvon Maday

We present a 3D hybrid method which combines the Finite Element Method (FEM) and the Spectral Boundary Integral method (SBIM) to model nonlinear problems in unbounded domains. The flexibility of FEM is used to model the complex,…

Numerical Analysis · Mathematics 2021-02-18 Gabriele Albertini , Ahmed Elbanna , David S. Kammer

In this paper, a novel feedback control-based particle filter algorithm for the continuous-time stochastic hybrid system estimation problem is presented. This particle filter is referred to as the interacting multiple model-feedback…

Numerical Analysis · Mathematics 2013-05-28 Tao Yang , Henk A. P. Blom , Prashant G. Mehta

In this work, we have presented a simple analytical approximation scheme for generic non-linear FBSDEs. By treating the interested system as the linear decoupled FBSDE perturbed with non-linear generator and feedback terms, we have shown…

Computational Finance · Quantitative Finance 2012-01-23 Masaaki Fujii , Akihiko Takahashi

In the last few decades, numerical simulation for nonlinear oscillators has received a great deal of attention, and many researchers have been concerned with the design and analysis of numerical methods for solving oscillatory problems. In…

Numerical Analysis · Mathematics 2020-12-25 Yu-Wen Li , Xinyuan Wu

A hybrid analytical method for solving linear and nonlinear fractional partial differential equations is presented. The proposed analytical method is an elegant combination of the Natural Transform Method (NTM) and a well-known method,…

General Mathematics · Mathematics 2018-04-17 Shehu Maitama

In this paper, we introduce a novel approach called the Iterative Aboodh Transform Method (IATM) which utilizes Daftardar--Jafari polynomials for solving non-linear problems. Such method is employed to derive solutions for non-linear…

Numerical Analysis · Mathematics 2025-02-18 Qasim Khan , Anthony Suen

This paper introduces HPIPM, a high-performance framework for quadratic programming (QP), designed to provide building blocks to efficiently and reliably solve model predictive control problems. HPIPM currently supports three QP types, and…

Optimization and Control · Mathematics 2020-06-09 Gianluca Frison , Moritz Diehl

The Asymptotic Iteration Method (AIM) is a technique for solving analytically and approximately the linear second-order differential equation, especially the eigenvalue problems that frequently appear in theoretical and mathematical…

Mathematical Physics · Physics 2020-03-17 Mourad E. H. Ismail , Nasser Saad

A lack of software reproducibility has become increasingly apparent in the last several years, calling into question the validity of scientific findings affected by published tools. Reproducibility issues may have numerous sources of error,…

Neurons and Cognition · Quantitative Biology 2020-04-23 Gregory Kiar , Pablo de Oliveira Castro , Pierre Rioux , Eric Petit , Shawn T. Brown , Alan C. Evans , Tristan Glatard

Efficient long-time integration of nonlinear fractional differential equations is significantly challenging due to the integro-differential nature of the fractional operators. In addition, the inherent non-smoothness introduced by the…

Numerical Analysis · Mathematics 2019-09-11 Yongtao Zhou , Jorge L. Suzuki , Chengjian Zhang , Mohsen Zayernouri

Many modern engineering structures exhibit nonlinear vibration. Characterizing such vibrations efficiently is critical to optimizing designs for reliability and performance. For linear systems, steady-state vibration occurs only at the…

Dynamical Systems · Mathematics 2024-05-02 Justin H. Porter , Matthew R. W. Brake

In this work we report on a new bootstrap method for quantum mechanical problems that closely mirrors the setup from conformal field theory (CFT). We use the equations of motion to develop an analogue of the conformal block expansion for…

High Energy Physics - Theory · Physics 2023-04-26 Colin Oscar Nancarrow , Yuan Xin

The fractional Fourier series generalizes the classical Fourier series by introducing a rotation angle $\alpha$ in the time-frequency plane, but inherits the Gibbs phenomenon for piecewise smooth functions. Unlike the classical setting, the…

Numerical Analysis · Mathematics 2026-05-13 Faiza Afzal , Xu Xiao

The coherent Ising machine (CIM) is a quantum-inspired computing platform that leverages optical parametric oscillation dynamics to solve combinatorial optimization problems by searching for the ground state of an Ising Hamiltonian.…

Quantum Physics · Physics 2025-09-18 Yan Chen Jiang , Lu Ma , Chuan Wang , Tie Jun Wang

We present a simple and easy to implement method for the numerical solution of a rather general class of Hamilton-Jacobi-Bellman (HJB) equations. In many cases, the considered problems have only a viscosity solution, to which, fortunately,…

Computational Finance · Quantitative Finance 2011-02-17 Jan Hendrik Witte , Christoph Reisinger

Fourier ptychographic microscopy (FPM) is a pivotal computational imaging technique that achieves phase and amplitude reconstruction with high resolution and wide field of view, using low numerical aperture objectives and LED array…