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What is HPM for Nonlinear ODE Solutions about?

The document outlines the application of the Homotopy Perturbation Method (HPM) to solve the ordinary differential equation dx/dt = x^2 + t with the initial condition x(0) = 0. It details the step-by-step process, including formulating the homotopy, assuming a series solution, equating coefficients, and constructing the approximate solution. The final approximate solution is given as x(t) ≈ t^2/2 + t^5/20 + t^8/160, with notes on convergence and practicality of the method.

Author

mmrmathsiubd

Language

EN