Tau Toolbox

Examples

Ordinary differential equations
Systems of ordinary differential equations
Nonlinear ordinary differential equations
Integro-differential equations
Systems of integro-differential equations
Nonlinear integro-differential equations

Systems of IDE

Example 1

Let us consider the linear system of integral equations $$ \begin{cases} \displaystyle y_1 - \int_{0}^{x}\left(\sin(x-t)-1\right)y_1(t)dt - \int_{0}^{x}\left(1-t\cos(x) \right)y_2(t)dt= g_1 \\ \displaystyle y_2 - \int_{0}^{x}y_1(t)dt - \int_{0}^{x}(x-t)y_2(t)dt= g_2 \end{cases}, $$ where $g_1 =-\frac{1}{2}(x-2)\sin(x) -x\cos(x) ^2+(\sin(x) +2)\cos(x) -1$ e $g_2 =-x+\sin(x) $. The next code presents the approximate solution by Tau Toolbox and the comparison with other autors: