Results 31 to 40 of about 6,277 (191)

Fast positive-real balanced truncation via quadratic alternating direction implicit iteration [PDF]

, 2007
Balanced truncation (BT), as applied to date in model order reduction (MOR), is known for its superior accuracy and computable error bounds. Positive-real BT (PRBT) is a particular BT procedure that preserves passivity and stability and imposes no ...
Balakrishnan, V, Wong, N
core   +1 more source

Numerical methods for time-fractional convection-diffusion problems with high-order accuracy

Open Mathematics, 2021
In this paper, we consider the numerical method for solving the two-dimensional time-fractional convection-diffusion equation with a fractional derivative of order α\alpha ...
Dong Gang, Guo Zhichang, Yao Wenjuan
doaj   +1 more source

An Unconditionally Stable Difference Scheme for the Two-Dimensional Modified Fisher–Kolmogorov–Petrovsky–Piscounov Equation

Journal of Mathematics, 2023
In this article, we develop an unconditionally stable numerical scheme for the modified Fisher–Kolmogorov–Petrovsky–Piscounov (Fisher–KPP) equation modeling population dynamics in two-dimensional space.
Soobin Kwak, Seungyoon Kang, Seokjun Ham, Youngjin Hwang, Gyeonggyu Lee, Junseok Kim   +5 more
doaj   +1 more source

ADI Compact Difference Scheme for the Two-Dimensional Integro-Differential Equation with Two Fractional Riemann–Liouville Integral Kernels

Fractal and Fractional
In this paper, a numerical method of a two-dimensional (2D) integro-differential equation with two fractional Riemann–Liouville (R-L) integral kernels is investigated. The compact difference method is employed in the spatial direction. The integral terms
Ziyi Chen, Haixiang Zhang, Hu Chen
doaj   +1 more source

Reflected Box Method: A Fast Quadratic‐Convergent Root Solver

The Journal of Engineering, Volume 2026, Issue 1, January/December 2026.
This article introduces the Reflected Box Method, a simple derivative–free root–finding algorithm based on geometric reflection and bracketing. The method achieves quadratic convergence using only basic arithmetic, making it suitable for embedded and fixed–point implementations.
Oswaldo Cadenas
wiley   +1 more source

An ADI extrapolated Crank-Nicolson orthogonal spline collocation method for nonlinear reaction-diffusion systems: a computational study

, 2012
An alternating direction implicit (ADI) orthogonal spline collocation (OSC) method is described for the approximate solution of a class of nonlinear reaction-diffusion systems.
Adomian, Amodio, Ang, Bialecki, Bialecki, Bialecki, Bialecki, Bruno, Crampin, Cui, Dang, de Boor, de Boor, Diaz, Diaz, Fairweather, Fernandes, Gao, Gierer, Graeme Fairweather, Gray, Gray, Hairer, Knezevic, Kondo, Lei, Liu, Lyon, Madzvamuse, McCourt, Mittal, Mittal, Nicolis, Peaceman, Pike, Polevikov, Qiao, Ruuth, Ryan I. Fernandes, Schnakenberg, Siraj-ul-Islam, Turing, Twizell, Verwer, Wang, Wang, Wazwaz, Yang, Zhang   +48 more
core   +1 more source

Cuckoo Search Optimized Fractional Physics‐Informed Neural Networks for Fourth‐Order Time‐Fractional Partial Differential Equations

Journal of Mathematics, Volume 2026, Issue 1, 2026.
Time‐fractional fourth‐order partial differential equations (PDEs) are typically important in the modeling of complex physical systems that have long‐memory effects and high‐order transverse spatial interaction. The paper presents a new hybrid method, called the Cuckoo Search–optimized fractional physics‐informed neural network (fPINN‐CS), that, to the
Ali Alkhathlan, Faris Kateb, Tauqeer Ahmad, Muhammad Sulaiman, Mohammed Abdullah Salman, Smritijit Sen   +5 more
wiley   +1 more source

Computational solutions of three-dimensional advection-diffusion equation using fourth order time efficient alternating direction implicit scheme

AIP Advances, 2017
To develop an efficient numerical scheme for three-dimensional advection diffusion equation, higher order ADI method was proposed. 2nd and fourth order ADI schemes were used to handle such problem.
Muhammad Saqib, Shahid Hasnain, Daoud Suleiman Mashat   +2 more
doaj   +1 more source

New high accuracy super stable alternating direction implicit methods for two and three dimensional hyperbolic damped wave equations

Results in Physics, 2014
In this paper, we report new three level implicit super stable methods of order two in time and four in space for the solution of hyperbolic damped wave equations in one, two and three space dimensions subject to given appropriate initial and Dirichlet ...
R.K. Mohanty
doaj   +1 more source

Total Value Adjustment of Multi-Asset Derivatives under Multivariate CGMY Processes

Fractal and Fractional, 2023
Counterparty credit risk (CCR) is a significant risk factor that financial institutions have to consider in today’s context, and the COVID-19 pandemic and military conflicts worldwide have heightened concerns about potential default risk.
Fengyan Wu, Deng Ding, Juliang Yin, Weiguo Lu, Gangnan Yuan   +4 more
doaj   +1 more source