Euler's Method for Numerical Analysis
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In numerical analysis, Euler's method serves as a fundamental numerical approach for solving differential equations. The core principle involves approximating derivatives using finite differences and iteratively computing solutions to converge toward the true answer. This algorithm finds practical applications in simulating dynamic systems across physics, biology, and engineering domains. MATLAB's robust numerical computation and visualization capabilities make it particularly suitable for implementing Euler's method. The implementation typically involves defining the differential equation function, setting initial conditions and step size, then iterating using the formula: y_{n+1} = y_n + h*f(x_n, y_n), where h represents the step size. Key MATLAB functions like plot() can visualize the numerical solution's progression against the analytical result for accuracy assessment.
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