Abstract
Purpose of study: To introduce the concept of projective and involuntary variational inequality problems of order and respectively. To study the equivalence theorem between these problems. To study the projected dynamical system using self involutory variational inequality problems.
 Methodology: Improved extra gradient method is used.
 Main Finding: Using a self-solvable improved extra gradient method we solve the variational inequalities. The algorithm of the projected dynamical system is provided using the RK-4 method whose equilibrium point solves the involutory variational inequality problems.
 Application of this study: Runge-Kutta type method of order 2 and 4 is used for the initial value problem with the given projected dynamical system with the help of self involutory variational inequality problems.
 The originality of this study: The concept of self involutory variational inequality problems, projective and involuntary variational inequality problems of order and respectively are newly defined.
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