9 articles
Adomian decomposition method
The Adomian decomposition method (ADM) is a semi-analytical technique for solving nonlinear differential and integral equations by expressing the solution as a series built recursively with Adomian polynomials, requiring no linearization or discretization.
Fixed-point iteration
Fixed-point iteration, also called Picard iteration or successive substitution, is a numerical method that solves equations by repeatedly applying a function to an initial guess.
Homotopy analysis method
The homotopy analysis method, developed by Shi-Jun Liao of Shanghai Jiaotong University in 1992, is a semi-analytical technique giving convergent series solutions of strongly nonlinear differential equations.
Homotopy method
A homotopy method, also called a continuation method, solves a system of equations by deforming an easy problem with known solutions into the target problem and tracking the solution paths.
Homotopy perturbation method
The homotopy perturbation method (HPM) is an analytical technique introduced by Ji-Huan He in 1999 that solves nonlinear differential equations without needing a small parameter.
Numerical continuation
Numerical continuation, also known as homotopy continuation, is a family of numerical methods that traces solution curves of parameterized nonlinear equations as a parameter varies, forming the basis of bifurcation analysis.
Residual power series method
The residual power series method (RPSM) is a semi-analytical technique that builds power series approximations to differential equations, fixing each coefficient by setting residual derivatives to zero.
Resummation
Resummation is a class of numerical and analytical methods that reorganize a divergent or slowly convergent series into a convergent approximation, chiefly through Borel summation.
Variational iteration method
The variational iteration method (VIM) is a semi-analytical technique for solving nonlinear differential and integral equations, introduced by Jihuan He in 1997, needing no linearization or small parameters.