Analysis for implicit and implicit-explicit ADER and DeC methods for ordinary differential equations, advection-diffusion and advection-dispersion equations

Authors: Philipp Öffner, Louis Petri, Davide Torlo

Source: Applied Numerical Mathematics. 212:110-134

Subject Terms: Method of lines for initial value and initial-boundary value problems involving PDEs, advection-diffusion, implicit-explicit methods, deferred correction, ADER, advection-dispersion, 65M06, 65M20, 65L05, 65L06, 65L07, Numerical Analysis (math.NA), stability, Numerical methods for initial value problems involving ordinary differential equations, Advection-diffusion, Advection-dispersion, Deferred correction, Implicit-explicit methods, Stability, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Finite difference methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, Mathematics - Numerical Analysis, Stability and convergence of numerical methods for ordinary differential equations

File Description: application/xml

Access URL: http://arxiv.org/abs/2404.18626
https://hdl.handle.net/11573/1747980
https://doi.org/10.1016/j.apnum.2024.12.013

Step-by-step time discrete Physics-Informed Neural Networks with application to a sustainability PDE model: Step-by-step time discrete physics-informed neural networks with application to a sustainability PDE model

Authors: Valentino C., Pagano G., Conte D., Paternoster B., Colace F., Casillo M.

Source: Mathematics and Computers in Simulation. 230:541-558

Subject Terms: Scientific machine learning, deep artificial neural networks, scientific machine learning, Stiff problems, Nonlinear sustainability PDE model, Implicit Euler and Crank–Nicolson methods, Deep artificial neural networks, Time discrete PINNs, Dye-sensitized solar cells, Numerical methods for initial value problems involving ordinary differential equations, nonlinear sustainability PDE model, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, time discrete PINNs, Finite difference methods for initial value and initial-boundary value problems involving PDEs, implicit Euler and Crank-Nicolson methods, Numerical investigation of stability of solutions to ordinary differential equations, dye-sensitized solar cells, stiff problems, Artificial neural networks and deep learning

File Description: application/xml

Access URL: https://hdl.handle.net/11588/995692
https://www.sciencedirect.com/science/article/pii/S0378475424004403

Numerical study of the fractional fourth-order evolution problems with weak singularity arises in chemical systems

Authors: Taneja, Komal, Chawla, Reetika, Kumar, Devendra, Vigo-Aguiar, J.

Source: Journal of Mathematical Chemistry. 63:1287-1311

Subject Terms: Numerical solution of boundary value problems involving ordinary differential equations, Fractional derivatives and integrals, graded mesh, time-fractional fourth order equation, stability and convergence, Numerical methods for initial value problems involving ordinary differential equations, evolution problems, quintic trigonometric B-spline, Caputo derivative, Numerical computation using splines

File Description: application/xml

Access URL: https://zbmath.org/8035161
https://doi.org/10.1007/s10910-025-01718-9

An improved fractional predictor-corrector method for nonlinear fractional differential equations with initial singularity

Authors: Jianfei Huang, Junlan Lv, Sadia Arshad

Source: Fractional Calculus and Applied Analysis. 28:453-472

Subject Terms: initial singularity, variable transformation, predictor-corrector method, error estimate, Numerical methods for initial value problems involving ordinary differential equations, Stability and convergence of numerical methods for ordinary differential equations, nonlinear fractional differential equation, Error bounds for numerical methods for ordinary differential equations

File Description: application/xml

Minimal $ \ell^2 $ norm discrete multiplier method: Minimal \(\ell^2\) norm discrete multiplier method

Authors: Schulz, Erick, Wan, Andy T. S.

Source: Journal of Computational Dynamics. 12:212-238

Subject Terms: Finite difference and finite volume methods for ordinary differential equations, Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems, Numerical Analysis, Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics), Simulation of dynamical systems, Numerical Analysis (math.NA), Dynamical Systems (math.DS), 65L05, 65L12, 65P10, 65Z05, 37M05, 37M15, 37N20, Numerical methods for Hamiltonian systems including symplectic integrators, Numerical methods for initial value problems involving ordinary differential equations, 01 natural sciences, dynamical system, Dynamical Systems, conservative integrator, pseudo inverse, Applications to the sciences, FOS: Mathematics, discrete multiplier method, Schwarzschild geodesic, conserved quantity, 0101 mathematics

File Description: application/xml

Access URL: http://arxiv.org/abs/2208.12355
https://zbmath.org/7978280
https://doi.org/10.3934/jcd.2024029

Stability Theory of TASE–Runge–Kutta Methods with Inexact Jacobian: Stability theory of TASE-Runge-Kutta methods with inexact Jacobian

Authors: Conte Dajana, Martin-Vaquero Jesus, Pagano Giovanni, Paternoster Beatrice

Source: SIAM Journal on Scientific Computing. 46:A3628-A3657

Subject Terms: Runge-Kutta methods, TASE operators, stiff problems, stability with inexact Jacobian, unconditional stability, field of values, Numerical Analysis (math.NA), Numerical methods for initial value problems involving ordinary differential equations, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Numerical methods for stiff equations, FOS: Mathematics, 65L04, 65L06, 65L07, 65L20, 65M12, 65M20, Mathematics - Numerical Analysis, Stability and convergence of numerical methods for ordinary differential equations

File Description: application/xml; application/pdf

Access URL: http://arxiv.org/abs/2401.10088
https://zbmath.org/7955197
https://doi.org/10.1137/24m1631869
https://hdl.handle.net/11588/995699
https://epubs.siam.org/doi/10.1137/24M1631869
https://epubs.siam.org/doi/10.1137/24M1631869
https://doi.org/10.1137/24M1631869
https://hdl.handle.net/11386/4889556
https://epubs.siam.org/doi/10.1137/24M1631869
https://hdl.handle.net/11588/995699
https://doi.org/10.1137/24M1631869

Error analysis of a high-order fully discrete method for two-dimensional time-fractional convection-diffusion equations exhibiting weak initial singularity

Authors: Singh, Anshima, Kumar, Sunil

Source: Numerical Algorithms. 99:251-284

Subject Terms: ADI scheme, error bound, high order, Numerical Analysis (math.NA), Numerical methods for initial value problems involving ordinary differential equations, fitted mesh, singularity, Caputo derivative, time-fractional convection-diffusion, Fractional derivatives and integrals, two-dimensional problems, FOS: Mathematics, Mathematics - Numerical Analysis, 65M06, 65M12, 65M70

File Description: application/xml

Access URL: http://arxiv.org/abs/2308.08971

Stability and numerical solutions for second-order ordinary differential equations with application in mechanical systems

Authors: Ali Turab, Andrés Montoyo, Josué-Antonio Nescolarde-Selva

Contributors: Universidad de Alicante. Departamento de Lenguajes y Sistemas Informáticos, Universidad de Alicante. Departamento de Matemática Aplicada, Procesamiento del Lenguaje y Sistemas de Información (GPLSI), Sistémica y Cibernética (SYC)

Source: RUA. Repositorio Institucional de la Universidad de Alicante
Universidad de Alicante (UA)

Subject Terms: Differential equations, Applications of boundary value problems involving ordinary differential equations, Generalized ordinary differential equations (measure-differential equations, set-valued differential equations, etc.), numerical computations, applications, differential equations, Stability analysis, Stability of solutions to ordinary differential equations, stability analysis, Numerical methods for initial value problems involving ordinary differential equations, 01 natural sciences, Solutions, Applications, 0103 physical sciences, Numerical computations, 0101 mathematics, solutions

File Description: application/xml

Access URL: http://hdl.handle.net/10045/144906
https://zbmath.org/8035095
https://doi.org/10.1007/s12190-024-02175-4

An innovative Fibonacci wavelet collocation method for the numerical approximation of Emden-Fowler equations

Authors: Manohara G, Kumbinarasaiah S

Source: Applied Numerical Mathematics. 201:347-369

Subject Terms: collocation method, Emden-Fowler equations, operational matrix of integration, Fibonacci wavelet, Numerical methods for initial value problems involving ordinary differential equations

File Description: application/xml

A posteriori error estimates and adaptivity for the continuous Galerkin time-stepping method for nonlinear initial value problems

Authors: Tian, Liutao, Yang, Shuo, Tian, Hongjiong

Source: Calcolo. 62

Subject Terms: Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations, continuous Galerkin method, initial value problem, Numerical methods for initial value problems involving ordinary differential equations, a posteriori error estimation, \textit{hp}-adaptive refinement procedure, Error bounds for numerical methods for ordinary differential equations

File Description: application/xml

Application of Spectral Collocation Method to Dynamic Comprehensive Stability Analysis of Fractional Diffusion-Reaction System: Application of spectral collocation method to dynamic comprehensive stability analysis of fractional diffusion-reaction system

Authors: Li, Shuo, Khan, Sami Ullah, Ismail, Emad A. A., Awwad, Fuad A., Yu, Jiamin, Sumelka, Wojciech

Source: International Journal of Theoretical Physics. 64

Subject Terms: Fractional derivatives and integrals, fractional diffusion-reaction equations, stability and quantitative analysis, spectral method, fractional calculus, Numerical methods for initial value problems involving ordinary differential equations

File Description: application/xml

Access URL: https://zbmath.org/8032276
https://doi.org/10.1007/s10773-025-05961-3

Investigation of the wavelet method impact on the mathematical model of global warming effects on marine ecosystems

Authors: S. Kumbinarasaiah, R. Yeshwanth

Source: Journal of Applied Mathematics and Computing. 70:4601-4627

Subject Terms: Caputo fractional derivative, collocation method, Numerical methods for wavelets, greenhouse gases, Haar wavelet, Fractional ordinary differential equations, operational matrix of integration, Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations, global warming, Numerical methods for initial value problems involving ordinary differential equations

File Description: application/xml

Access URL: https://zbmath.org/8035075
https://doi.org/10.1007/s12190-024-02147-8

Computational and analytical analysis of integral-differential equations for modeling avoidance learning behavior

Authors: Ali Turab, Andrés Montoyo, Josué-Antonio Nescolarde-Selva

Contributors: Universidad de Alicante. Departamento de Lenguajes y Sistemas Informáticos, Universidad de Alicante. Departamento de Matemática Aplicada, Procesamiento del Lenguaje y Sistemas de Información (GPLSI), Sistémica y Cibernética (SYC)

Source: RUA. Repositorio Institucional de la Universidad de Alicante
Universidad de Alicante (UA)

Subject Terms: 0301 basic medicine, 0303 health sciences, Applications of boundary value problems involving ordinary differential equations, Generalized ordinary differential equations (measure-differential equations, set-valued differential equations, etc.), numerical computations, Avoidance behavior, avoidance behavior, Numerical methods for initial value problems involving ordinary differential equations, Solutions, 03 medical and health sciences, Fixed-point theorems, integral-differential equations, Integral-differential equations, Numerical computations, solutions

File Description: application/xml

Access URL: http://hdl.handle.net/10045/143517
https://zbmath.org/8035067
https://doi.org/10.1007/s12190-024-02130-3

Delay-dependent stability of a class of Runge-Kutta methods for neutral differential equations

Authors: Wang, Zheng, Cong, Yuhao

Source: Numerical Algorithms. 98:1643-1666

Subject Terms: Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, delay-dependent stability, argument principle, TASE-RK, Numerical methods for functional-differential equations, TASE-W, Numerical methods for initial value problems involving ordinary differential equations, Stability and convergence of numerical methods for ordinary differential equations, neutral delay differential equation, Neutral functional-differential equations

File Description: application/xml

Access URL: https://zbmath.org/8015092
https://doi.org/10.1007/s11075-024-01846-4

Developing a continuous SIR epidemic model and its discrete version using Euler method: Analyzing dynamics with analytical and numerical methods: Developing a continuous SIR epidemic model and its discrete version using Euler method: analyzing dynamics with analytical and numerical methods

Authors: Fatemeh Sahaminejad, Nemat Nyamoradi, Zohreh Eskandari

Source: Mathematical Methods in the Applied Sciences. 47:10320-10333

Subject Terms: 0301 basic medicine, analytical methods, continuous and discrete-time models, 0303 health sciences, 03 medical and health sciences, Epidemiology, numerical methods, Euler method, SIR epidemic model, Numerical methods for initial value problems involving ordinary differential equations, Dynamical systems in biology, dynamics analysis, 3. Good health

File Description: application/xml

A Generalized Single‐Step Multi‐Stage Time Integration Formulation and Novel Designs With Improved Stability and Accuracy: A generalized single-step multi-stage time integration formulation and novel designs with improved stability and accuracy

Authors: Yazhou Wang, Nikolaus A. Adams, Kumar K. Tamma

Source: International Journal for Numerical Methods in Engineering. 126

Subject Terms: Finite difference methods applied to problems in solid mechanics, RESEARCH ARTICLE, consistency analysis, local truncation error, multi-stage time integration algorithms, order reduction, structural dynamics, Numerical methods for initial value problems involving ordinary differential equations, ddc

File Description: application/xml; application/pdf

Access URL: https://mediatum.ub.tum.de/1780394

A high-order multi-resolution wavelet method for nonlinear systems of differential equations

Authors: Muhammad Ahsan, Weidong Lei, Martin Bohner, Amir Ali Khan

Source: Mathematics and Computers in Simulation. 215:543-559

Subject Terms: collocation method, KdV equations (Korteweg-de Vries equations), Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations, Numerical methods for wavelets, H-HWCM, Haar wavelet, system of nonlinear differential equations, quasi-linearization technique, Numerical methods for initial value problems involving ordinary differential equations, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs

File Description: application/xml

High-order compact difference schemes based on the local one-dimensional method for high-dimensional nonlinear wave equations

Authors: Wu, Mengling, Wang, Zhi, Ge, Yongbin

Source: Computational Geosciences. 27:687-705

Subject Terms: Finite difference methods for boundary value problems involving PDEs, fourth-order compact scheme, high-dimensional nonlinear wave equation, variable coefficient, Finite difference methods for initial value and initial-boundary value problems involving PDEs, local one-dimensional, Wave equation, PDEs in connection with fluid mechanics, Numerical methods for initial value problems involving ordinary differential equations

File Description: application/xml

Constructing time integration with controllable errors for constrained mechanical systems

Authors: Xiaoming Xu, Yanghui Chen, Jiahui Luo, Jiafu Liu, Haijun Peng, Zhigang Wu

Source: Applied Mathematical Modelling. 118:185-211

Subject Terms: Numerical methods for differential-algebraic equations, 0203 mechanical engineering, generalized constraint forces, Numerical integration, 0103 physical sciences, 02 engineering and technology, differential algebraic equations (DAEs), augmented Lagrangian formulations, symplectic integration, Numerical methods for initial value problems involving ordinary differential equations, Lagrange's equations, Lagrange d'Alembert principle, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/7682526
https://doi.org/10.1016/j.apm.2023.01.037

Computing the Lyapunov operator φ-functions, with an application to matrix-valued exponential integrators: Computing the Lyapunov operator \(\varphi \)-functions, with an application to matrix-valued exponential integrators

Authors: Dongping Li, Yue Zhang, Xiuying Zhang

Source: Applied Numerical Mathematics. 182:330-343

Subject Terms: Numerical computation of matrix exponential and similar matrix functions, \( \varphi \)-functions, G.1.7, G.1.3, modified scaling and squaring method, Numerical Analysis (math.NA), Numerical methods for initial value problems involving ordinary differential equations, 01 natural sciences, 65F30, 65F10, 65L05, 15A60, Lyapunov operator, FOS: Mathematics, matrix-valued exponential integrators, Mathematics - Numerical Analysis, 0101 mathematics

File Description: application/xml

Access URL: http://arxiv.org/abs/2204.12976