Galerkin method for constrained variational equations and a collage-based approach to related inverse problems

DOI10.1016/j.cam.2015.06.016zbMath1327.65138OpenAlexW1045366343MaRDI QIDQ495049

Yong-Cai Geng, Sumit K. Garg

Publication date: 9 September 2015

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

Full work available at URL: https://doi.org/10.1016/j.cam.2015.06.016

zbMATH Keywords

inverse problemsboundary value problemsreflexive Banach spacesimpulsive differential equationsvariational equations with constraints

Mathematics Subject Classification ID

Variational inequalities (49J40) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Duality and reflexivity in normed linear and Banach spaces (46B10) Boundary value problems with impulses for ordinary differential equations (34B37) Numerical solution of inverse problems involving ordinary differential equations (65L09)

Related Items (14)

Solving inverse problems for steady-state equations using a multiple criteria model with collage distance, entropy, and sparsity ⋮ Inverse problems via the ``generalized collage theorem for vector-valued Lax-Milgram-based variational problems ⋮ An efficient and robust numerical solver for impulsive control of fractional chaotic systems ⋮ Solving inverse problems for mixed-variational equations on perforated domains ⋮ A minimax approach for inverse variational inequalities ⋮ A perturbed collage theorem and its application to inverse interval integral problems ⋮ Using the generalized collage theorem for estimating unknown parameters in perturbed mixed variational equations ⋮ Fractal-based methods and inverse problems for differential equations: current state of the art ⋮ Convergence and Data Dependency of Normal−S Iterative Method for Discontinuous Operators on Banach Space ⋮ An inverse problem for Bingham type fluids ⋮ Numerical method and convergence order for second-order impulsive differential equations ⋮ Optimization methods in inverse problems and applications to science and engineering ⋮ Reconstruction analysis of honeybee colony collapse disorder modeling ⋮ Numerical solution for an inverse variational problem

Cites Work

• Unnamed Item
• A sequential approach for solving the Fredholm integro-differential equation
• Characterization of the solvability of generalized constrained variational equations
• A generalized collage method based upon the Lax-Milgram functional for solving boundary value inverse problems
• Galerkin schemes and inverse boundary value problems in reflexive Banach spaces
• Solving inverse problems for variational equations using ``generalized collage methods, with applications to boundary value problems
• Solving inverse problems for DEs using the collage theorem and entropy maximization
• Variational approach to impulsive differential equations
• High-order nonlinear initial-value problems countably determined
• Numerical treatment of fixed point applied to the nonlinear Fredholm integral equation
• Nonlinear Volterra integral equation of the second kind and biorthogonal systems
• Biorthogonal systems approximating the solution of the nonlinear Volterra integro-differential equation
• A collage-based approach to solving inverse problems for second-order nonlinear parabolic PDEs
• Mixed variational formulations in locally convex spaces
• Solving inverse problems for biological models using the collage method for differential equations
• Fixed point techniques and Schauder bases to approximate the solution of the first order nonlinear mixed Fredholm-Volterra integro-differential equation
• Inverse problems for ODEs using contraction maps and suboptimality of the  collage method
• Solution of an inverse problem for fractals and other sets
• Solving inverse problems for ordinary differential equations using the Picard contraction mapping

This page was built for publication: Galerkin method for constrained variational equations and a collage-based approach to related inverse problems