What is the concept of order of convergence in Numerical Analysis?

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What is the concept of order of convergence in Numerical Analysis?

The concept of order of convergence in Numerical Analysis refers to the rate at which a numerical method or algorithm converges to the true solution of a mathematical problem. It measures how quickly the error decreases as the number of iterations or steps increases. The order of convergence is typically denoted by the symbol "p" and can be determined by analyzing the behavior of the error as the step size or grid size approaches zero. A higher order of convergence indicates faster convergence and better efficiency of the numerical method.