Newton's method for nonlinear ordinary and partial differential equations

DOI10.1016/0022-247X(79)90059-3zbMath0416.65074MaRDI QIDQ754625

To-yat Cheung

Publication date: 1979

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

Newton's methodapproximate solutionsa- posteriori error boundsinverse-positive propertylocal, uniform and quadratic convergencenonlinear ordinary or partial differential equationsquasilinear elliptic, parabolic and hyperbolic problems

Mathematics Subject Classification ID

Numerical solutions to equations with nonlinear operators (65J15) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Differential inequalities involving functions of a single real variable (34A40) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) Numerical methods for partial differential equations, boundary value problems (65N99)

Cites Work

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• Elliptic boundary value problems suggested by nonlinear diffusion processes
• Solution of monotone nonlinear elliptic boundary value problems
• Newton's method for convex nonlinear elliptic boundary value problems
• Approximate solutions and error bounds for quasilinear elliptic boundary value problems
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• Three Nonlinear Initial Value Problems of the Hyperbolic Type
• Approximate Solutions and Error Bounds for Quasi-Linear Hyperbolic Initial Boundary Value Problems
• Boundary Value Problems for Ordinary Differential Equations
• Quasilinear Parabolic Boundary Value Problems. Approximate Solutions and Error Bounds by Linear Programming
• General boundary value problems for elliptic partial differential equations