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Introduction

Definition

Example 01

Example 02

Example 03

Example 04

Example 05

Example 06

Example 07

Example 08

Example 09

Example 10

Example 11

Example 12

Example 13

Example 14

Example 15

Example 16

Example 17

Example 18

References

Example 18

Integrate[{s, 0, t}]


GIVEN: One ODE

REQUIRED: Solve it

SOLUTION: Generate example18.nb

x0 = 1;
a = 2;
f[t_] = Sin[t];
op[x_] := x0 - a*Integrate[x, {s, 0, t}] + Integrate[f[s], {s, 0, t}];
exact = DSolve[{x'[t] + a * x[t] == f[t], x[0] == x0}, x[t], t];
x = 7 + 8 t;
xx = ToString[x];
aa = ToString[a];
ff = ToString[f[t]];
Print[""]
g = x /. t -> s;
Print["Start of Iteration ...."]
Print["Initial guess: x[t] =", x]
graph = {};
Do[S = op[g];
si = ToString[i];
llabel = StringJoin["Exact and Approx solns when i = ", si];
If[Mod[i, 3] < 1,
graph = Append[graph, Plot[{x[t] /. exact, S}, {t, 0, 1},
PlotLabel -> llabel, PlotRange -> All, DisplayFunction -> Identity]]
];
g = S /. t -> s, {i, 12}]
graph1 = Partition[graph, 2];
output = Show[GraphicsArray[graph1],
DisplayFunction -> $DisplayFunction]

Example

Homework:

a. Change the initial condition

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