Computing Methods, Volume 2Computing Methods, Volume I generalizes and details the methods involved in computer mathematics. The book has been developed in two volumes; Volume I contains Chapters 1 to 5, and Volume II encompasses Chapters 6 to 10. |
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Page 302
... derivatives of up to order n in the region under consideration . The required solution will then have continuous derivatives of up to order n + 1 , and we can write : △ y 。= y ( x ) — Y。= ( x − x 。) Y % + ( x - x6 ) 2 2 ! yő + ...
... derivatives of up to order n in the region under consideration . The required solution will then have continuous derivatives of up to order n + 1 , and we can write : △ y 。= y ( x ) — Y。= ( x − x 。) Y % + ( x - x6 ) 2 2 ! yő + ...
Page 444
... derivatives can be obtained by differentiating the Laplace operator . For this we need to put c2 = 1 6h2 Then for co and c1 we have : 10 2 Co and ; C1 = 3h2 3h2 whilst h2 2 zu , = ( usi + uj ) , + 12 ( dra + dy3 ) ( wx + uji )。 + + x2 ...
... derivatives can be obtained by differentiating the Laplace operator . For this we need to put c2 = 1 6h2 Then for co and c1 we have : 10 2 Co and ; C1 = 3h2 3h2 whilst h2 2 zu , = ( usi + uj ) , + 12 ( dra + dy3 ) ( wx + uji )。 + + x2 ...
Page 488
... derivatives ce and select them so ди ди J2u and Эх ду дх ду disappear after entering the expansions on the right - hand side , whilst the terms with second - order derivatives give the operator Lu . For this , we require that co , C1 ...
... derivatives ce and select them so ди ди J2u and Эх ду дх ду disappear after entering the expansions on the right - hand side , whilst the terms with second - order derivatives give the operator Lu . For this , we require that co , C1 ...
Contents
The Squareroot Method | 16 |
Conjugate Gradients | 23 |
Partitioning into SubMatrices | 34 |
Copyright | |
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a₁ absolute magnitude approximate solution arbitrary b₁ boundary conditions boundary nodes boundary value problem C₁ C₂ calculations Cauchy problem characteristic polynomial coefficients column consider constant convergence corresponding defined derivatives difference equation difference scheme differential equations Dirichlet problem dx dy eigenvalues eigenvectors elements equal error estimate exact solution find the solution formula Goursat problem inequality initial conditions initial vector integral equation internal nodes interval iteration J²u K(xn k₁ linear algebraic linear algebraic equations matrix mesh method method of solving multiplied norm obtained operator orthogonal Poisson's equation presupposed real roots region G right-hand side sequence set of equations set of linear straight line Substituting Suppose we put symmetric Taylor formula theorem U₁ vector x₁ y₁ zero ду дх მყ