Asymptotic Analysis & Adomian Decomposition: Explained

[chwala]

Asymptotic analysis
Hi,
can someone please give me a highlight of asymptotic analysis and singular cauchy problems...how is asymptotic compared to convergence...to my understanding when you have a polynomial divided by a polynomial= solution + remainder...the solution is the asymptotic and the remainder the error btwn the exact value and the asymptote..kindly advice.
i also need advice on adomian convergence concept.

regards,
chwala kennedy MSC APPLIED MATHEMATICS FINALIST Kenyatta University,Kenya

 

[gtoguy97]

.Asymptotic analysis is a branch of mathematics that studies the behavior of functions as they approach infinity or zero. It is used to understand the behavior of a system in the limit, and can be used to determine the optimal values of certain parameters. Asymptotic analysis can also be used to analyze the convergence of sequences or series.Singular Cauchy problems involve finding solutions to equations with singularities or discontinuities. These problems can be solved using techniques like the Laplace transform, Fourier transform, or Adomian decomposition. Convergence is a concept related to asymptotic analysis. It is used to describe the behavior of a sequence or series as it approaches its limit as the number of terms gets larger and larger. Adomian decomposition is a technique for solving nonlinear equations. It involves approximating the equation by an infinite series, which is then solved term-by-term. This method can be used to solve many types of equations, including singular Cauchy problems.