A5070164432- Numerical methods for differential equations
- Differential Equations and Numerical Methods
- Advanced Numerical Methods in Computational Mathematics
- Matrix Theory and Algorithms
- Differential Equations and Boundary Problems
- Advanced Mathematical Modeling in Engineering
- Computational Fluid Dynamics and Aerodynamics
- Spectral Theory in Mathematical Physics
- Electromagnetic Simulation and Numerical Methods
- Nonlinear Differential Equations Analysis
- Space Satellite Systems and Control
- Astro and Planetary Science
- Nonlinear Waves and Solitons
- Fractional Differential Equations Solutions
- Model Reduction and Neural Networks
- Advanced Fiber Laser Technologies
- Electromagnetic Scattering and Analysis
- Numerical methods in engineering
- Planetary Science and Exploration
- Numerical methods in inverse problems
- Advanced Fiber Optic Sensors
- Nonlinear Photonic Systems
- Photonic and Optical Devices
- Total Knee Arthroplasty Outcomes
- Membrane-based Ion Separation Techniques
TU Wien
2014-2024
University of Florence
2015-2020
Liceo scientifico statale Ulisse Dini
2010-2020
Palacký University Olomouc
2015
Technische Universität Braunschweig
2015
University of Bari Aldo Moro
2015
University of Salento
2015
Institute for Scientific Analysis
2009
We consider overdetermined collocation methods and propose a weighted least squares approach to derive numerical solution. The discrete problem requires the evaluation of Jacobian vector field which, however, appears in O(h) term, h being stepsize. show that, by neglecting this infinitesimal resulting scheme becomes low-rank Runge–Kutta method. Among possible choices weights distribution, we analyze one based on quadrature formula underlying conditions. A few illustrations are included...
Analytical properties like existence, uniqueness and smoothness of continuous solutions nonlinear boundary value problems are considered. Fredholm theory for linear is established. The results applied to two practical examples from the spherical shells.
The collocation methods for solving linear boundary value problems with a singularity of the first kind are investigated. stability and convergence results established. Particular attention is paid to superconvergence properties methods, which different as in classical case when not present. extended nonlinear illustrated by numerical examples.
We discuss an a posteriori error estimate for the numerical solution of boundary value problems nonlinear systems ordinary differential equations with singularity first kind. The global approximation obtained by collocation piecewise polynomial functions is based on defect correction principle. prove that methods which are not superconvergent, asymptotically correct. As essential prerequisite we derive convergence results applied to singular problems.
We discuss the properties of differential equation , a.e. on where and satisfies -Carathéodory conditions for some . A full description asymptotic behavior functions satisfying is given. also describe structure boundary which are necessary sufficient to be at least in As an application theory, new existence and/or uniqueness results solutions periodic value problems shown.
We investigate the convergence properties of iterated defect correction (IDeC) method based on implicit Euler rule for solution singular initial value problems with a singularity first kind. show that retains its classical order convergence, which means sequence approximations obtained during iteration shows gradually growing limited by smoothness data and technical details procedure.
Abstract We consider systems of integral-algebraic and integro-differential equations with weakly singular kernels. Although these problem classes are not in the focus main stream literature, they interesting, only their own right, but also because may arise from analysis certain differential-algebraic partial differential equations. In first part paper, we deal two-dimensional Next, analyze Volterra integral kind which determinant kernel matrix k(t, x) vanishes when t = x. Finally, third...
We investigate the convergence properties of single and multiple shooting when applied to singular boundary value problems. Particular attention is paid well-posedness process. It shown that problems can be solved efficiently a high order integrator for associated initial available. Moreover, results perturbed Newton iteration are discussed.