Related papers: Numerical Issues for a Non-autonomous Logistic Mod…

For a large class of fully nonlinear parabolic equations, which include gradient flows for energy functionals that depend on the solution gradient, the semidiscretization in time by implicit Runge-Kutta methods such as the Radau IIA methods…

Designing robust space trajectories in nonlinear dynamical environments, such as the Earth-Moon circular restricted three-body problem (CR3BP), poses significant challenges due to sensitivity to initial conditions and non-Gaussian…

This work introduces a new class of Runge-Kutta methods for solving nonlinearly partitioned initial value problems. These new methods, named nonlinearly partitioned Runge-Kutta (NPRK), generalize existing additive and component-partitioned…

This work is devoted to find the numerical solutions of several one dimensional second-order ordinary differential equations. In a heuristic way, in such equations the quadratic logistic maps regarded as a local function are inserted within…

Simulations of biophysical systems inevitably include steps that correspond to time integrations of ordinary differential equations. These equations are often related to enzyme action in the synthesis and destruction of molecular species,…

Identifying governing equations in physical and biological systems from datasets remains a long-standing challenge across various scientific disciplines, providing mechanistic insights into complex system evolution. Common methods like…

We provide a note on continuous-stage Runge-Kutta methods (csRK) for solving initial value problems of first-order ordinary differential equations. Such methods, as an interesting and creative extension of traditional Runge-Kutta (RK)…

This paper investigates the performance of a subclass of exponential integrators, specifically explicit exponential Runge--Kutta methods. It is well known that third-order methods can suffer from order reduction when applied to linearized…

The optimal control of a mechanical system is of crucial importance in many realms. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion…

Nonlinear programming problems are useful in designing and assigning work schedule and also in transporting goods and services from known sources to specified destinations. The objective function could be linear or nonlinear depending on…

In order to solve continuous-time optimal control problems, direct methods transcribe the infinite-dimensional problem to a nonlinear program (NLP) using numerical integration methods. In cases where the integration error can be manipulated…

This paper illuminates the derivation, the applicability, and the efficiency of the Multiplicative Runge-Kutta Method, derived in the frame- work of geometric multiplicative calculus. The removal of the restrictions of geometric…

Finite element discretization of time dependent problems also require effective time-stepping schemes. While implicit Runge-Kutta methods provide favorable accuracy and stability problems, they give rise to large and complicated systems of…

A computational revolution unleashed the power of artificial neural networks. At the heart of that revolution is automatic differentiation, which calculates the derivative of a performance measure relative to a large number of parameters.…

This article extends the theory of dual-consistent summation-by-parts (SBP) and generalized SBP (GSBP) time-marching methods by showing that they are implicit Runge-Kutta schemes. Through this connection, the accuracy theory for the…

Logistic regression is a well-known statistical model which is commonly used in the situation where the output is a binary random variable. It has a wide range of applications including machine learning, public health, social sciences,…

Meta-learning has emerged as an important framework for learning new tasks from just a few examples. The success of any meta-learning model depends on (i) its fast adaptation to new tasks, as well as (ii) having a shared representation…

A focus of recent research in quantum computing has been on developing quantum algorithms for differential equations solving using variational methods on near-term quantum devices. A promising approach involves variational algorithms, which…

The study of the dynamics of the size of a population via mathematical modelling is a problem of interest and widely studied. Traditionally, continuous deterministic methods based on differential equations have been used to deal with this…

Mutualistic communities have an internal structure that makes them resilient to external per- turbations. Late research has focused on their stability and the topology of the relations between the different organisms to explain the reasons…