# Solver document

## XLPack Solver

XLPack solver is the add-in program to help use XLPack without VBA programming for nonlinear equations, nonlinear optimization, nonlinear least squares problems, quadrature and ordinary differential equations. This add-in is included in XLPack Module 3 and 4 packages and XLPack Lite. Note – XLPack solver manipulates a current worksheet (active worksheet) only. Even if a […]

## XLPack Solver – General Nonlinear Equation

Solve the general nonlinear equation with single variable using Dfzero. Let’s solve the following example equation. f(x) = x^3 – 2x – 5 = 0 The solver program will write the value of x into the variable value cell (B6 in this case). The function value cell (B7 in this case) must contain the formula […]

## XLPack Solver – System of Nonlinear Equations

Solve the system of nonlinear equations (find the real solution). Let’s solve the following example. f1(x1,x2) = 4*x1^2 + x2^2 – 16 f2(x1,x2) = x1^2 + x2^2 – 9 The solver program will write the value of x1 and x2 into the variable value cells (B8 and B9 in this case). The function value cells […]

## XLPack Solver – Univariate Nonlinear Optimization

Minimize the nonlinear function with single variable using Dfmin. Let’s find the minimum point of the following example equation. f(x) = x^3 – 2x – 5 The solver program will write the value of x into the variable value cell (B6 in this case). The function value cell (B7 in this case) must contain the […]

## XLPack Solver – Multivariate Nonlinear Optimization

Minimize the nonlinear function with multiple variables. Let’s find the minimum point of the following example equation. f(x1,x2) = 100*(x2 – x1^2)^2 + (1 – x1)^2 (Rosenbrock function) The solver program will write the value of x1 and x2 into the variable value cells (B8 and B9 in this case). The function value cell (C8 […]

## XLPack Solver – Nonlinear Least Squares Problems

Solve the nonlinear lease squares problems. Let’s solve the following example (Reference: https://www.itl.nist.gov/div898/strd/nls/data/misra1a.shtml). Find the parameters p1 and p2 to approximate the following data using the model function f(x) = p1*(1 – exp(-p2*x)) with least sum of squares of residuals. x y 77.6 10.07 114.9 14.73 141.1 17.94 190.8 23.93 239.9 29.61 289.0 35.18 332.8 […]

## XLPack Solver – Quadrature (finite interval)

Compute the numerical integration of the given function. Let’s compute the integral of the following example function. f(x) = 1/(1 + x^2) The solver program will write the value of x into the variable value cell (B6 in this case). The function value cell (B7 in this case) must contain the formula to compute f(x) […]

## XLPack Solver – Quadrature (semi-infinite interval)

This function computes the numerical integration of the given function over a semi-infinite interval (one of the interval bounds is -∞ or +∞). Let’s compute the integral of the following example function. f(x) = 1/(1 + x^2) The solver program will write the value of x into the variable value cell (B6 in this case). […]

## XLPack Solver – Quadrature (infinite interval)

This function computes the numerical integration of the given function over an infinite interval (both interval bounds are infinite). Let’s compute the integral of the following example function. f(x) = 1/(1 + x^2) The solver program will write the value of x into the variable value cell (B6 in this case). The function value cell […]

## 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) […]

## XLPack Solver – Save/restore Parameters

By saving the input parameters in each menu of XLPack solver into the worksheet, you can save time and effort to set the parameters each time by restoring all parameter values. Click “Save/Restore” in the dialog of each function. Select appropriate cell range (A10:A13 in this example) and click “Save” to save input parameters into […]