Euler's Method is a numerical technique used to approximate solutions to ordinary differential equations (ODEs) by iteratively advancing a solution over small steps, using the slope at the current point to estimate the next point. It is a straightforward method that is easy to implement but can accumulate significant errors, especially for stiff or highly nonlinear equations.

Euler's Method

numerical technique

Ordinary Differential Equations (ODEs) are equations involving functions of one independent variable and their derivatives, representing a wide range of physical phenomena and mathematical models. Solving ODEs is fundamental in fields such as physics, engineering, and economics, providing insights into dynamic systems and processes.

ordinary differential equations

ODEs

approximate solutions

iteratively advancing a solution

small steps

slope at the current point

estimate the next point

straightforward method

easy to implement

significant errors

Stiff equations are a class of differential equations where certain numerical methods for solving them become unstable unless the step size is taken to be extremely small. They often arise in systems with widely varying timescales, requiring specialized solvers to efficiently and accurately capture the dynamics without excessive computational cost.

Stiff Equations

highly nonlinear equations

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