Design and implementation of a general interpreter for step-by-step solving of nonlinear system of equations using symbolic approaches

In this work, we present the design and implementation of an interpreter program for the step-by-step numerical solutions of nonlinear systems of equations with multiple variables, using symbolic computation methods and automatic code generation tools. The development process starts with a representation of a nonlinear system of equations in a formal language in terms of context-free grammars then, a parser which is generated via the JavaCC tool is used to represent the nonlinear system of equations in the form of object structures. The numerical method Newton-Raphson are employed to obtain better approximations to solutions of nonlinear systems. The interpreter can easily be extended to cover other numerical methods, only describing the related iterative computation steps. On the other hand, integrating into their own interactive development environments, researchers can input any system of nonlinear equations directly into the interpreter and get the approximating solution as an output. Key words: Symbolic computation, system of nonlinear equations, step-by-step Solution, Newton-Raphson method, parser, context-free grammars.