Numerical Solution of Differential Equations

absolute value accuracy Adams-Moulton Akad analytic apply boundary conditions boundary values C₁ calculation characteristic numbers coefficients Collatz column components constant convergence correct CORRECTOR Cowell-Crommelin denote derivatives difference equation digits equa estimate Example formula function given heat equation Hence illustrate initial values initial vector interior points interval iteration Laplace's equation latent roots latent vectors linear machine Math Mathematics method of Article Method VII Milne Monte Carlo method Nauk numerical integration numerical methods numerical solution obtained operator ordinary differential equations orthogonal parabolic partial differential equations Poisson's equation polynomial PREDICTOR problem procedure quadrature formulas r₁ r₂ region residuals round-off round-off error seventh order Simpson's rule solution of differential solve stability step length symmetric symmetric matrix Table Taylor's series Theorem tion truncation error U₁ Y₁ yn+1 zero λε λη λι