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A Discussion on numerical analysis of partial
O B Widlund 167177
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accuracy algorithms approximate solution asymptotic error expansions basis functions behaviour boundary conditions boundary-value problems Bramble calculation Cauchy problem coefficients Comput conservation consider constant Crank-Nicolson derivatives difference approximations difference equations difference operators difference scheme dimensions Dirichlet Dirichlet boundary conditions Dirichlet problem discrete discussed dtf-iv elliptic error bound example extrapolation figure finite finite-difference methods finite-difference scheme finite-difference solution finite-element method flow fluid formula Fort-Frankel Galerkin Galerkin method given Green's formula grid length harmonic mixed heat equation hopscotch hyperbolic inequality initial instability integral equation interaction interior interpolation Kreiss Laplace's equation Lax-Wendroff method Lax-Wendroff scheme Math matrix mesh mesh-points non-negative nonlinear norm numerical analysis numerical solution obtained one-dimensional paper partial differential equations Pereyra points polynomials practical region requires Richardson extrapolation satisfy singularities solving space spline stability conditions step subspace sufficiently smooth techniques Theorem truncation error value problem variables wave Wendroff zero