Numerical Methods: Boundary Value Problems

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Introduces the finite difference method for approximating derivatives and solving differential equations in practical applications.

Explores the heat equation in 1D, emphasizing conservation of thermal energy and numerical solution methods.

Covers numerical methods for solving boundary value problems using finite difference, FFT, and finite element methods.

Explains finite difference grids for computing solutions of elastic membranes using Laplace's equation and numerical methods.

Covers non-linear ordinary differential equations, including separation, Cauchy problems, and stability conditions.

Covers the stability analysis of ODEs using numerical methods and discusses stability conditions.

Explores inverse monotonicity in numerical methods for differential equations, emphasizing stability and convergence criteria.

Covers the basics of Partial Differential Equations, focusing on heat transfer modeling and numerical solution methods.

Covers error division and schemes for solving differential equations.

Discusses the numerical analysis of pollutant transport equations and their applications in environmental modeling.