COLLOCATION APPROXIMATIONS FOR WEAKLY SINGULAR VOLTERRA INTEGRO‐DIFFERENTIAL EQUATIONS

A piecewise polynomial collocation method for solving linear weakly singular integro‐differential equations of Volterra type is constructed. The attainable order of convergence of collocation approximations on arbitrary and quasi‐uniform grids is studied theoretically and numerically.

Fourth and Fifth Order Double Burmester Points and the Highest Attainable Order of Straight Lines

This paper addresses the problems of fourth and fifth order double Burmester points. It also presents a general treatment to elaborate Mueller’s concepts on the highest attainable order of straight lines. The treatment is made possible with the derivation of a bi-quadratic equation whose four roots representing the four Burmester points in a planar motion. The subjects are complex but the treatment is simple and no complex geometry is involved. The results are general and applicable to any general planar motion rather than limited to four-bar linkages. Simple synthesis techniques are demonstrated in examples and the inverse Euler-Savary equation is introduced as a convenient feature in synthesis.