A guide to
analytical methods.
Six ways to approach nonlinear differential equations. Learn the intuition, follow a worked example and understand the limits before applying a method.
Akbari–Ganji method
Turn a differential equation into a carefully chosen algebraic problem.
Homotopy perturbation method
Build a difficult solution from a sequence of simpler equations.
Variational iteration method
Use the equation’s residual to improve an initial guess.
Homotopy analysis method
Add an explicit parameter for controlling a series construction.
Differential transform method
Compute a local power series through coefficient recurrences.
Adomian decomposition method
Decompose the solution and its nonlinearity together.
Explore an equation.
Understand the approximation.
Compare an approximation with a reference solution. The difference is part of the lesson.
Explore the equation
An answer is only
the beginning.
Model
State the assumptions, parameters and initial or boundary conditions.
Approximate
Choose a method and a trial or expansion that fits the problem.
Verify
Check the residual and conditions. Compare with an independent reference.
Understand
Test convergence, identify the useful domain and explain the physical meaning.