How to change font size for abstract title

Here it is.

Simply modify the meaning of abstract by inserting the following lines in your preamble:

\makeatletter
\renewenvironment{abstract}{%
    \if@twocolumn
      \section*{\abstractname}%
    \else %% <- here I've removed \small
      \begin{center}%
        {\bfseries \Large\abstractname\vspace{\z@}}%  %% <- here I've added \Large
      \end{center}%
      \quotation
    \fi}
    {\if@twocolumn\else\endquotation\fi}
\makeatother

MWE:

%%%%****This is my code*****
\documentclass[10pt]{article}
\usepackage{multicol}
\setlength{\columnsep}{20.0pt}
 \title{some title}

\makeatletter
\renewenvironment{abstract}{%
    \if@twocolumn
      \section*{\abstractname}%
    \else %% <- here I've removed \small
      \begin{center}%
        {\bfseries \Large\abstractname\vspace{\z@}}%  %% <- here I've added \Large
      \end{center}%
      \quotation
    \fi}
    {\if@twocolumn\else\endquotation\fi}
\makeatother

\begin{document}
\maketitle
  %%this this title haven't the correct size
\begin{abstract}
    this abstract have the correct size
\end{abstract}
\begin{multicols}{2}


\section{introduction}%%this title have the correct size
some introduction.

Whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever.
\section{another section}
Whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever, whatever
\end{multicols}
\end{document}

Output:

It's worth examining how the abstract environment is defined by the article document class:

\if@titlepage
  \newenvironment{abstract}{%
      \titlepage
      \null\vfil
      \@beginparpenalty\@lowpenalty
      \begin{center}%
        \bfseries \abstractname
        \@endparpenalty\@M
      \end{center}}%
     {\par\vfil\null\endtitlepage}
\else
  \newenvironment{abstract}{%
      \if@twocolumn
        \section*{\abstractname}%
      \else
        \small
        \begin{center}%
          {\bfseries \abstractname\vspace{-.5em}\vspace{\z@}}%
        \end{center}%
        \quotation
      \fi}
      {\if@twocolumn\else\endquotation\fi}
\fi

In your case, since neither the titlepage nor the twocolumn options are in effect, the definition works out to be

 \newenvironment{abstract}{%
        \small
        \begin{center}%
          {\bfseries \abstractname\vspace{-.5em}\vspace{\z@}}%
        \end{center}%
        \quotation
      }
      {\endquotation}

The upshot is that if neither the titlepage nor the twocolumn options are in effect, (a) the relative font size is changed to \small, (b) the abstract's title (given by \abstractname) is centered, and (c) the body of the abstract is typeset inside a quotation environment; most importantly, this means that the margins inside the abstract environment are bit wider (and the text block is a bit narrower) than they are in the body of the text.

If you prefer the "look" that's produced if the twocolumn option is set, just issue the following instruction (in the preamble):

\renewenvironment{abstract}{\section*{\abstractname}}{}

Or, even more simply, just don't use the abstract environment at all. Instead, simply type

\section*{\abstractname}

followed by the body of the abstract.

Another two solutions that are not looking at the internals, but just imitate them. One for a regular twocolumn (documentclass option) document, one for an imitated twocolumn document (using package multicol).

\documentclass[10pt,twocolumn]{article}
\usepackage{blindtext}
\usepackage{titling}
\title{Wombats are cool}

\renewcommand{\maketitlehookd}{%
    \begin{center}\normalfont\Large\bfseries\centering Abstract\end{center}
    \begin{quotation}
        \blindtext
    \end{quotation}
}
\begin{document}
\maketitle


\section{Introduction}
\blindtext[2]
\section{Capybara}
\blindtext
\end{document}

Using package multicol, note the different margins.

\documentclass[10pt]{article}
\usepackage{blindtext}
\usepackage{multicol}
\setlength{\columnsep}{20.0pt}
\title{K\"urbiskernbr\"otchen}

\begin{document}
\maketitle
\begin{center}\normalfont\Large\bfseries\centering Abstract\end{center}
\begin{quotation}
    \blindtext
\end{quotation}

\begin{multicols}{2}

    \section{Introduction}
    Whenever, whereever, we're meant to be together
    \blindtext
    \section{Wombat}
    \blindtext
\end{multicols}
\end{document}