## Three-step Exponentially Fitted Second Derivative for Solving Volterra Integral Equation of the Second Kind

Raymond, Dominic *

Department of Mathematics and Statistics, Federal University Wukari, Wukari, Nigeria.

Ajia, Rita

Department of Mathematics and Statistics, College of Agriculture, Science and Technology, Jalingo, Nigeria.

Adu, Agyemang

Department of Mathematics and Statistics, Federal University Wukari, Wukari, Nigeria.

*Author to whom correspondence should be addressed.

### Abstract

This paper uses the interpolation and collocation method approach to develop an exponentially fitted second derivative hybrid block method for the solution of Volterra integral equations of the second kind. When the continuous block techniques were placed at each location, the discrete block methods were discovered. Each discrete scheme obtained from the simultaneous solution of the block and techniques used to implement the main method has the same level of accuracy as the main continuous method. As a result, a new class of three-step two off-grid points procedures was developed, each of which provided stable intervals of absolute stability and a high order of accuracy with a very low error constant. The basic properties of the methods were investigated and were found to be zero-stable, consistent and convergent. On a few Volterra integral equations of the second kind issues, the effectiveness of the techniques was evaluated. The numerical experimental results observe that our methods gives better approximation than the existing method compared with.

Keywords: Three-step, exponenetiall block approach, Volterra integral equation

**How to Cite**

*Asian Journal of Pure and Applied Mathematics*,

*5*(1), 251–263. Retrieved from https://globalpresshub.com/index.php/AJPAM/article/view/1831

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