The decomposition method for Cauchy advection-diffusion problems

DOI10.1016/j.camwa.2004.10.031zbMath1138.65307OpenAlexW2114009939MaRDI QIDQ2485430

Daniel Lesnic

Publication date: 4 August 2005

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2004.10.031

zbMATH Keywords

Inverse problemsAdvection-diffusion equationDecomposition methodCharacteristic and noncharacteristic Cauchy problemsVariable flow velocity

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Initial value problems for second-order parabolic equations (35K15) Basic methods in fluid mechanics (76M99)

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Cites Work

• Modification of the decomposition approach to the heat equation
• A new approach to the heat equation - an application of the decomposition method
• Application of decomposition to convection-diffusion equations
• Adomian's method of decomposition: Critical review and examples of failure
• Solving frontier problems modelled by nonlinear partial differential equations
• The decomposition approach to inverse heat conduction
• The noisy convergence phenomena in decomposition method solutions
• Application of the decomposition method to the solution of the reaction- convection-diffusion equation
• Mathematical Analysis: An Inverse Problem Arising in Convective-Diffusive Flow
• A mollified method for the solution of the Cauchy problem for the convection–diffusion equation
• Entry and Exit Conditions for Flow Reactors
• New analytic solutions of the one-dimensional heat equation for temperature and heat flow rate both prescribed at the same fixed boundary (with applications to the phase change problem)
• On the Cauchy Problem for the One-Dimensional Heat Equation