Multistep Methods of the Hybrid Type and Their Application to Solve the Second Kind Volterra Integral Equation

There are some classes of methods for solving integral equations the variable boundaries. It is known that each method has its own advantages and disadvantages. By taking into account disadvantages methods, here was constructed a new free from them. For this, we have used multistep advanced hybrid types construction with best properties intersection We also show connection which using initial-value problem ODEs first order. Some been applied to solve model problems. A formula proposed determine maximal values order accuracy stable unstable here. Note construct propose use system algebraic allows us by minimal volume computational works at step. more exact second derivative method, comparisons methods. formulas accuracy, determined necessary sufficient conditions convergence One can proved usually ODE, demonstrating applications these Volterra integro-differential equations. illustration results, concrete one them equation.