Continuous multistep methods for volterra integro-differential equations of the second order

A new class of numerical methods for Volterra integro-differential equations of the second order is developed. The methods are based on interpolation and collocation of the shifted Legendre polynomial as basis function with Trapezoidal quadrature rules. The convergence analysis revealed that the methods are consistent and zero stable, hence their convergence. Numerical examples revealed that the methods compared favourably with existing standard methods.