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1: 3.6 Linear Difference Equations

… ►Then $w_n$ is said to be a recessive (equivalently, minimal or distinguished) solution as $n\to \mathrm{\infty }$, and it is unique except for a constant factor. … …

2: 37.20 Mathematical Applications

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Numerical Solution of Differential Equations

►OPs are used in collocation method or spectral method for numerical solution of partial differential equations. … ►A minimal cubature rule is a numerical integration rule that uses the smallest number of nodes among cubature rules of the same degree. …Although Gaussian cubature rules rarely exist and they do not exist for centrally symmetric domains, minimal or near minimal cubature rules on the unit square are known and provide efficient numerical integration rules. …

3: Bibliography S

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Asymptotic solutions of nonlinear evolution equations and a Painlevé transcendent. Phys. D 3 (1-2), pp. 165–184.

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External Links:

Document, ZentralBlatt

Referenced by:

§32.11(ii).

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Flux vacua and branes of the minimal superstring. J. High Energy Phys. 2005 (01), pp. 1–37.

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Notes:

Electronic. E-print number: hep-th/0412315. 38 pp.

External Links:

Link, ISSN 1126-6708, Document, MathReview (S. Yu. Alexandrov)

Referenced by:

§32.16.

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Lamé polynomial solutions to some elliptic crack and punch problems. Internat. J. Engrg. Sci. 16 (8), pp. 551–563.

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External Links:

ISSN 0020-7225, Document, MathReview, ZentralBlatt

Referenced by:

§29.19(ii).

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The computation of eigenvalues and solutions of Mathieu’s differential equation for noninteger order. ACM Trans. Math. Software 19 (3), pp. 377–390.

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External Links:

ISSN 0098-3500, Document, ZentralBlatt

Referenced by:

item (e).

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The linear differential equation whose solutions are the products of solutions of two given differential equations. J. Math. Anal. Appl. 98 (1), pp. 130–147.

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External Links:

ISSN 0022-247X, Document, FullText, MathReview (Wolfgang Bühring), ZentralBlatt

Referenced by:

§1.13(v).

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4: 3.11 Approximation Techniques

… ►Then there exists a unique $n$th degree polynomial $p_n(x)$, called the minimax (or best uniform) polynomial approximation to $f(x)$ on $[a,b]$, that minimizes ${\max }_{a\le x\le b}\left|{ϵ}_n(x)\right|$, where ${ϵ}_n(x)=f(x)-p_n(x)$. … ►of type $[k,\mathrm{\ell }]$ to $f$ on $[a,b]$ minimizes the maximum value of $\left|{ϵ}_{k,\mathrm{\ell }}(x)\right|$ on $[a,b]$, where … ►With $b_0=1$, the last $q$ equations give $b_1,\mathrm{\dots },b_q$ as the solution of a system of linear equations. … ►that minimizes … ►of given functions ${\varphi }_k(x)$, $k=0,1,\mathrm{\dots },n$, that minimizes …

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