PIECEWISE-POLYNOMIAL SOLUTIONS OF THE PARTIAL DIFFERENTIAL EQUATIONS
Piecewise-polynomial approximation of the partial differential equations (DE) is based on Newton's interpolation polynomial. At the current subdomain on grid approximations all partial DE derivatives are interpolated, coefficients of the interpolation polynomial are calculated, the solution is approached with iterated integral. The process is repeated iteratively until the approximation error of the second derivative is minimized. Computer realization has highly accurate approximation of the solution at a low time complexity.