Solving numerically nonlinear systems of balance laws by multivariate sigmoidal functions approximation

DOI10.1007/s40314-016-0334-8zbMath1395.65115OpenAlexW2323427369MaRDI QIDQ1655363

Renato Spigler, Danilo Costarelli

Publication date: 9 August 2018

Published in: Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40314-016-0334-8

zbMATH Keywords

logistic functionsunit step functionsGompertz functionsmultivariate sigmoidal functions approximationnonlinear systems of balance laws

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Approximation by other special function classes (41A30) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99)

Related Items (9)

Approximation theorems for a family of multivariate neural network operators in Orlicz-type spaces ⋮ Novel bifurcation results for a delayed fractional-order quaternion-valued neural network ⋮ Convergence for a family of neural network operators in Orlicz spaces ⋮ An efficient asymptotic-numerical method to solve nonlinear systems of one-dimensional balance laws ⋮ Superposition, reduction of multivariable problems, and approximation ⋮ A collocation method for solving nonlinear Volterra integro-differential equations of neutral type by sigmoidal functions ⋮ Interpolation by neural network operators activated by ramp functions ⋮ The max-product generalized sampling operators: convergence and quantitative estimates ⋮ Approximate solutions of Volterra integral equations by an interpolation method based on ramp functions

Cites Work

• On the Hausdorff distance between the Heaviside step function and Verhulst logistic function
• Asymptotic-numerical solution of nonlinear systems of one-dimensional balance laws
• Solving Volterra integral equations of the second kind by sigmoidal functions approximation
• Approximation results for neural network operators activated by sigmoidal functions
• Multivariate neural network operators with sigmoidal activation functions
• Approximation by superposition of sigmoidal and radial basis functions
• Balancing source terms and flux gradients in high-resolution Godunov methods: The quasi-steady wave-propagation algorithm
• Univariant approximation by superpositions of a sigmoidal function
• Neural network operators: constructive interpolation of multivariate functions
• Global smooth solutions to the multi-dimensional hydrodynamic model for two-carrier plasmas
• Entropy and global existence for hyperbolic balance laws
• Interpolation by neural network operators activated by ramp functions
• Convergence of a family of neural network operators of the Kantorovich type
• Approximation by series of sigmoidal functions with applications to neural networks
• A collocation method for solving nonlinear Volterra integro-differential equations of neutral type by sigmoidal functions
• Max-product neural network and quasi-interpolation operators activated by sigmoidal functions
• Localization effects and measure source terms in numerical schemes for balance laws
• The Large-Time Behavior of the Scalar, Genuinely Nonlinear Lax-Friedrichs Scheme
• Universal approximation bounds for superpositions of a sigmoidal function
• Stable Solutions for a Catalytic Converter
• Convergence of the $2 \times 2$ Godunov Method for a General Resonant Nonlinear Balance Law
• A review of numerical methods for nonlinear partial differential equations
• Constructive Approximation by Superposition of Sigmoidal Functions
• Numerical methods for nonconservative hyperbolic systems: a theoretical framework.
• The Formation and Decay of Shock Waves
• Mathematical modeling in economics, ecology and the environment
• Approximation by superpositions of a sigmoidal function
• Approximation by superpositions of a sigmoidal function
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