Accuracy and Stability: Algorithms Performance

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Explicit Stabilised Methods: Stochastic Differential Equations

Covers explicit stabilized methods for stiff stochastic differential equations, analyzing their properties and applications.

Ordinary Differential Equations: Methods and Applications

Explores ordinary differential equations and numerical integration methods for stability and accuracy.

Zero-stability and absolute-stability

Explores zero-stability and absolute-stability in numerical methods, including Forward Euler, Backward Euler, Crank-Nicolson, and Heun's methods.

Runge Kutta and Multistep Methods

Explores Runge Kutta and multistep methods for solving ODEs, including Backward Euler and Crank-Nicolson.

Elements of computational complexity

Covers classical and quantum computational complexity concepts and implications.

Scientific Computing in Neuroscience

Explores scientific computing in neuroscience, emphasizing the simulation of neurons and networks using tools like NEURON, NEST, and BRIAN.

Finite Element Modeling: Dynamics

Introduces the basics of finite element modeling for dynamics and discusses the Newmark method for time integration.

Factoring Polynomials: Complexity and Algorithms

Delves into the complexity of factoring polynomials and the implications for security.

Error Estimation in Numerical Methods

Explores error estimation in numerical methods for solving ordinary differential equations, emphasizing the impact of errors on solution accuracy and stability.

Classical Mechanics and Molecular Dynamics

Covers classical mechanics, molecular dynamics, integrators, constant-temperature simulations, and melting point calculations for aluminum.