Modeling Software

EQUATRAN is a software application for solving sets of mathematical equations. It has been extensively used for many years by Japanese chemical companies and is applicable for engineering applications in the fields of chemical, mechanical, or electrical engineering.

It can be used in the following situations:

• Spreadsheets such as Excel are convenient to use to solve simple problems, but for more complex problems it can be time-consuming to set up. Equations must be rearranged, careful thought must be given to the order in which equations are solved, and iterative calculations can be time-consuming. It is difficult to track the calculation logic in the spreadsheet if the problem contains many variables, and mistakes can easily be made which may go unnoticed.
• Programming languages such as Visual Basic are convenient to solve any type of engineering calculation, but the programming for daily engineering tasks for various calculations tend to consume time. As with a spreadsheet solution, complex problems need to be carefully constructed and can take a lot of time to prepare.
• For chemical engineers, a process simulator is rigorous and makes it easy to calculate unit operations such as distillation. This is an appropriate tool for an engineering department, but engineers in other departments such as process development and production needs to handle many other unit operations. Process simulators offer rigid and inflexible models and are often difficult to customise.
• It is sometimes necessary to develop your own model to simulate the phenomena and improve operations in the plant. EQUATRAN offers a flexible environment to solve simultaneous non-linear equations, differential equations and to solve optimisation problems.

EQUATRAN can perform equation solving using mathematical language similar to that we all learned at school. For instance "2x+3y=9" can be written "2*x+3*y=9" and "dC/dt=-kC" can be written "C′=-k*C". Simply type the equations, and provided that the system is solvable, EQUATRAN will return the values of all variables.

It also has the capability to optimise an objective function, which for example, can be used to find the reaction kinetic parameters for experimental data with known reaction equations.

Modeling by Use of Equations

It is possible to obtain direct numerical solutions simply by entering equations. Equations can be modeled as they are, and can be solved without being modified or rearranged.

Solving a Variety of Equations without Specifying Solver

It is possible to solve systems of linear equations, nonlinear simultaneous equations and ordinary differential equations.
Multivariable optimization problems and least squares problems can also be handled. In addition, these types of problems can be handled in combination.
Unlike other commercial software which require the specification of the solver according to the type of the problems, EQUATRAN solve all these equations without specifying the solver.

Obtaining Solutions in a Shorter Period of Time than with a Programming Language

When solving problems with a programming language, it is necessary to think out the algorithm that uses the numerical calculation method, and to create a program based on the syntax of the language. In EQUATRAN-G you will get an answer in a shorter period of time because this troublesome work is entirely automated.

Wide Range of Applications

EQUATRAN can be applied to design and analysis problems such as curve fitting to make approximations from data, balance calculations and equilibrium calculations, or the dynamic simulation of continuous systems.

Functions

Simultaneous Linear Equations

There is no rule for the order in which simultaneous linear equations are written. EQUATRAN features a unique function with the ability to determine which set of equations is to be solved simultaneously or to be calculated by rearranging them. It is also able to identify whether the simultaneous equations are a linear or non-linear type and select a calculation method to solve the equations. To solve simultaneous linear equations, for instance, the Gauss' elimination method is automatically selected and applied.

Simultaneous Non-Linear Equations

Solving simultaneous non-linear equations is just as simple. The iteration method, in general, is necessary to solve them; calculations are repeatedly performed until convergence is reached. To perform this, the improved Newton-Raphson Method is automatically selected. Iterative procedures are created so as to minimize the number of variables that represent initial estimate values and to reduce the calculation amount. In addition, EQUATRAN allows users to specify variable names as well as equations that are used to check the convergence, and yet calculation results are obtained quickly and accurately.

Ordinary Differential Equations

The initial value problem of an ordinary differential equation can be solved numerically. By using symbols such as x' for dx/dt and x" for d2x/dt2, the high-order ordinary differential equations as well as their simultaneous equations can be written without having to modify them. In addition, three different integration methods, including Euler, Runge-Kutta (RK) and Variable Step RK, are incorporated and selected accordingly.

Optimization

EQUATRAN can solve non-linear optimization problems determining the variable values that minimize or maximize the evaluation function value. It can also solve the optimization problems involved with multiple independent variables and inequalities. As effective calculation methods, Complex for general optimization problems and Marquardt, which enables the non-linear least-squares method to be quickly performed, are available.

Compound-Complex Problems

The compound-complex problems with a combination of ordinary differential equations and linear/non-linear equations, the simu taneous non-linear equations involved in the calculation of an optimization problem, etc., can be solved by simply writing them in lines. With user-defined functions, more complex problems, such as multiple integrals, two-point boundary value and mini-max problems, parameter identification in dynamic systems, can be solved. In addition, EQUATRAN can handle large-scale models with more than 1000 equations.

System Configuration

• OS: Microsoft Windows 10 / 8.1 / 7
• Hard disk with unused memory capacity of at least 10MB
• Microsoft Windows-compatible display monitor, printer and mouse