# XLPack Solver – Ordinary Differential Equations (ODEs)

Compute the solution of the initial value problem of the ordinary differential equations.

Let’s solve the following example equations.

dy1/dt = -y2, dy2/dt = y1
where y1 = 1, y2 = 0 at t0 = 0

The solver program will write the value of t into the independent variable (t) cell (B8 in this case) and the values of yi into the dependent variable (yi) cells (B9 and B10 in this case). The differential equation (dyi/dt) cells (B13 and B14 in this case) must contain the formulas to compute dy1/dt and dy2/dt from t and yi. To solve this example, the formula for B13 is =-B10 and that for B14 is =B9.

The initial values and output range (D8:F28 in this case) is the cell range for the value of t (input) in the first column and the computed values of yi in the second, third, … columns (output). Input the initial values (t0, y1 at t0 and y2 at t0 in this case) in the first row and the target t value in the first column of second and later rows, and click “Compute”. Then the values of yi at t of each row will be computed and output to the second and later columns of each row. If the row with a blank cell in the first column is encountered, the computation will be terminated even within the initial value and output range.

Derkf, Dopri5, Dop853, Deabm, Debdf (for stiff problem) and Radau (for stiff problem) can be selected as the solver program.

The standard value of tolerance is 1.0e-8. The tolerance value will be set to RTol and ATol of each routine.

The cell ranges can be specified as larger than required. In that case, only the necessary range will be used from left upper corner. Please refer to here for “Save/Restore” button.

When “Help” button is clicked, this page will be displayed if the network connection is available.

The “?” button of right upper corner will not work correctly. Please use “Help” button.