- - - Department Mathematics, Education College for pure Sciences, Basrah University, Basrah, Iraq
- - - Open Education College in Basrah, Basrah, Iraq

The goal of this study is to expand the usage of a collection method based on shifted Legendre polynomials in matrix form to approximate the derivative to obtain numerical solutions for the unsteady state one-dimensional bioheat equation. The proposed methodology is used to two examples to illustrate its utility and accuracy. The numerical results shown that the techniques used are effective as well as gives high accuracy and good convergence

Collocation method, bioheat equation, Legendre Polynomials, Accuracy