Boundary Problems in 1D: Finite Differences

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

Explores boundary value problems, finite difference method, and Joule heating examples in 1D.

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

Discusses finite differences and finite elements, focusing on variational formulation and numerical methods in engineering applications.

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

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

Covers Euler and Crank-Nicolson methods for solving differential equations.

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

Explores numerical methods like Crank-Nicolson, Heun, Euler, and RK4 for solving ODEs, emphasizing error estimation and convergence.

Covers the Cauchy problem in differential equations, focusing on initial conditions and their impact on solution uniqueness.