(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 9.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       157,          7]
NotebookDataLength[      4092,        130]
NotebookOptionsPosition[      3849,        117]
NotebookOutlinePosition[      4193,        132]
CellTagsIndexPosition[      4150,        129]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[
 RowBox[{
  RowBox[{"RK4", "[", 
   RowBox[{"f_", ",", "u0_", ",", "h_", ",", "t0_", ",", "T_"}], "]"}], ":=", 
  RowBox[{"(", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"n", "=", 
     RowBox[{"Ceiling", "[", 
      RowBox[{
       RowBox[{"(", 
        RowBox[{"T", "-", "t0"}], ")"}], "/", "h"}], "]"}]}], ";", 
    "\[IndentingNewLine]", 
    RowBox[{"t", "=", 
     RowBox[{"Table", "[", 
      RowBox[{
       RowBox[{"i", " ", "h"}], ",", 
       RowBox[{"{", 
        RowBox[{"i", ",", "0", ",", "n"}], "}"}]}], "]"}]}], ";", 
    "\[IndentingNewLine]", 
    RowBox[{"y", "=", 
     RowBox[{"Table", "[", 
      RowBox[{"0", ",", 
       RowBox[{"{", 
        RowBox[{"n", "+", "1"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{"y", "[", 
      RowBox[{"[", "1", "]"}], "]"}], "=", "u0"}], ";", "\[IndentingNewLine]", 
    RowBox[{"For", "[", 
     RowBox[{
      RowBox[{"i", "=", "1"}], ",", 
      RowBox[{"i", "\[LessEqual]", "n"}], ",", 
      RowBox[{"i", "++"}], ",", "\[IndentingNewLine]", 
      RowBox[{
       RowBox[{"k1", "=", 
        RowBox[{"h", " ", 
         RowBox[{"f", "[", 
          RowBox[{
           RowBox[{"t", "[", 
            RowBox[{"[", "i", "]"}], "]"}], ",", 
           RowBox[{"y", "[", 
            RowBox[{"[", "i", "]"}], "]"}]}], "]"}]}]}], ";", 
       "\[IndentingNewLine]", 
       RowBox[{"k2", "=", 
        RowBox[{"h", " ", 
         RowBox[{"f", "[", 
          RowBox[{
           RowBox[{
            RowBox[{"t", "[", 
             RowBox[{"[", "i", "]"}], "]"}], "+", 
            RowBox[{"h", "/", "2"}]}], ",", 
           RowBox[{
            RowBox[{"y", "[", 
             RowBox[{"[", "i", "]"}], "]"}], "+", 
            RowBox[{"k1", "/", "2"}]}]}], "]"}]}]}], ";", 
       "\[IndentingNewLine]", 
       RowBox[{"k3", "=", 
        RowBox[{"h", " ", 
         RowBox[{"f", "[", 
          RowBox[{
           RowBox[{
            RowBox[{"t", "[", 
             RowBox[{"[", "i", "]"}], "]"}], "+", 
            RowBox[{"h", "/", "2"}]}], ",", 
           RowBox[{
            RowBox[{"y", "[", 
             RowBox[{"[", "i", "]"}], "]"}], "+", 
            RowBox[{"k2", "/", "2"}]}]}], "]"}]}]}], ";", 
       "\[IndentingNewLine]", 
       RowBox[{"k4", "=", 
        RowBox[{"h", " ", 
         RowBox[{"f", "[", 
          RowBox[{
           RowBox[{
            RowBox[{"t", "[", 
             RowBox[{"[", "i", "]"}], "]"}], "+", "h"}], ",", 
           RowBox[{
            RowBox[{"y", "[", 
             RowBox[{"[", "i", "]"}], "]"}], "+", "k3"}]}], "]"}]}]}], ";", 
       "\[IndentingNewLine]", 
       RowBox[{
        RowBox[{"y", "[", 
         RowBox[{"[", 
          RowBox[{"i", "+", "1"}], "]"}], "]"}], "=", 
        RowBox[{
         RowBox[{"y", "[", 
          RowBox[{"[", "i", "]"}], "]"}], "+", 
         RowBox[{
          FractionBox["1", "6"], 
          RowBox[{"(", 
           RowBox[{"k1", "+", 
            RowBox[{"2", "k2"}], "+", 
            RowBox[{"2", "k3"}], "+", "k4"}], ")"}]}]}]}]}]}], 
     "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", "y"}], 
   "\[IndentingNewLine]", ")"}]}]], "Input",
 CellChangeTimes->{{3.664889161346874*^9, 3.6648892186583633`*^9}, {
  3.6691041921064377`*^9, 3.669104263666531*^9}}]
},
WindowSize->{1920, 998},
WindowMargins->{{-8, Automatic}, {Automatic, -8}},
FrontEndVersion->"10.1 for Microsoft Windows (64-bit) (March 23, 2015)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[557, 20, 3288, 95, 386, "Input"]
}
]
*)

(* End of internal cache information *)