W. S. Loud

1.4k total citations · 1 hit paper
31 papers, 952 citations indexed

About

W. S. Loud is a scholar working on Applied Mathematics, Numerical Analysis and Geometry and Topology. According to data from OpenAlex, W. S. Loud has authored 31 papers receiving a total of 952 indexed citations (citations by other indexed papers that have themselves been cited), including 14 papers in Applied Mathematics, 11 papers in Numerical Analysis and 9 papers in Geometry and Topology. Recurrent topics in W. S. Loud's work include Advanced Differential Equations and Dynamical Systems (8 papers), Differential Equations and Numerical Methods (7 papers) and Numerical methods for differential equations (7 papers). W. S. Loud is often cited by papers focused on Advanced Differential Equations and Dynamical Systems (8 papers), Differential Equations and Numerical Methods (7 papers) and Numerical methods for differential equations (7 papers). W. S. Loud collaborates with scholars based in United States and Italy. W. S. Loud's co-authors include C. R. Wylie, J. C. Jaeger, P. R. Sethna, A. G. Sveshnikov, A. B. Vasil’eva and André Vanderbauwhede and has published in prestigious journals such as Journal of Applied Mechanics, Annals of Mathematics and SIAM Review.

In The Last Decade

W. S. Loud

31 papers receiving 772 citations

Hit Papers

align trajectories

What are hit papers?

Hit papers significantly outperform the citation benchmark for their cohort. A paper qualifies if it has ≥500 total citations, achieves ≥1.5× the top-1% citation threshold for papers in the same subfield and year (this is the minimum needed to enter the top 1%, not the average within it), or reaches the top citation threshold in at least one of its specific research topics.

Advanced Engineering Mathematics.

1952 542 citations W. S. Loud, C. R. Wylie American Mathematical Monthly profile →

Peers — A (Enhanced Table)

Peers by citation overlap · career bar shows stage (early→late) cites · hero ref

Name	h						Papers	Cites
W. S. Loud United States	13	149	143	143	129	125	31	952
R. V. Churchill United States	6	143 1.0×	104 0.7×	176 1.2×	124 1.0×	107 0.9×	13	1.3k
IH Parker United Kingdom	5	80 0.5×	195 1.4×	114 0.8×	73 0.6×	88 0.7×	5	692
Richard C. Roberts United Kingdom	7	92 0.6×	107 0.7×	71 0.5×	52 0.4×	108 0.9×	11	919
W. Nachbar United States	12	131 0.9×	280 2.0×	123 0.9×	83 0.6×	207 1.7×	32	1.4k
J.R. Kuttler United States	19	106 0.7×	94 0.7×	159 1.1×	74 0.6×	114 0.9×	47	1.5k
Lawrence E. Levine United States	5	143 1.0×	319 2.2×	146 1.0×	266 2.1×	75 0.6×	15	1.4k
Karel Rektorys Czechia	8	83 0.6×	119 0.8×	103 0.7×	32 0.2×	68 0.5×	17	684
P. M. Prenter United States	11	77 0.5×	331 2.3×	136 1.0×	195 1.5×	64 0.5×	25	1.1k
H. Kagiwada United States	21	159 1.1×	206 1.4×	192 1.3×	72 0.6×	33 0.3×	109	1.3k
J. S. Shipman United States	12	79 0.5×	312 2.2×	81 0.6×	53 0.4×	71 0.6×	25	950

Countries citing papers authored by W. S. Loud

Since Specialization

Citations

This map shows the geographic impact of W. S. Loud's research. It shows the number of citations coming from papers published by authors working in each country. You can also color the map by specialization and compare the number of citations received by W. S. Loud with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites W. S. Loud more than expected).

Fields of papers citing papers by W. S. Loud

Since Specialization

Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by W. S. Loud. Nodes represent research fields, and links connect fields that are likely to share authors. Colored nodes show fields that tend to cite the papers produced by W. S. Loud. The network helps show where W. S. Loud may publish in the future.

Co-authorship network of co-authors of W. S. Loud

This figure shows the co-authorship network connecting the top 25 collaborators of W. S. Loud. A scholar is included among the top collaborators of W. S. Loud based on the total number of citations received by their joint publications. Widths of edges represent the number of papers authors have co-authored together. Node borders signify the number of papers an author published with W. S. Loud. W. S. Loud is excluded from the visualization to improve readability, since they are connected to all nodes in the network.

All Works

Sort: Min cites: Since: Top N: Style:

20 of 20 papers shown

1.

Loud, W. S., et al.. (1987). Differential Equations.. American Mathematical Monthly. 94(3). 308–308. 14 indexed citations

2.

Loud, W. S.. (1984). Subharmonic solutions of second-order equations arising near harmonic solutions. Journal of Differential Equations. 53(2). 192–212. 2 indexed citations

3.

Loud, W. S. & André Vanderbauwhede. (1983). Functional dependence and boundary-value problems with families of solutions. Journal of Differential Equations. 47(3). 444–461. 1 indexed citations

4.

Loud, W. S.. (1980). A Bifurcation Application of the Generalized Inverse of a Linear Differential Operator. SIAM Journal on Mathematical Analysis. 11(3). 545–558. 2 indexed citations

5.

Loud, W. S.. (1976). Branching of solutions of two-parameter boundary-value problems for second order differential equations. Archive of Applied Mechanics. 45(5-6). 347–359. 2 indexed citations

6.

Loud, W. S.. (1975). Stability regions for Hill's equation. Journal of Differential Equations. 19(2). 226–241. 16 indexed citations

7.

Loud, W. S.. (1972). Subharmonic solutions of second order equations arising near harmonic solutions. Journal of Differential Equations. 11(3). 628–660. 5 indexed citations

8.

Loud, W. S.. (1970). Some Examples of Generalized Green’s Functions and Generalized Green’s Matrices. SIAM Review. 12(2). 194–210. 25 indexed citations

9.

Loud, W. S.. (1969). Nonsymmetric periodic solutions of certain second order nonlinear differential equations. Journal of Differential Equations. 5(2). 352–368. 3 indexed citations

10.

Loud, W. S.. (1966). Generalized Inverses and Generalized Green’s Functions. SIAM Journal on Applied Mathematics. 14(2). 342–369. 20 indexed citations

11.

Loud, W. S. & P. R. Sethna. (1966). Some explicit estimates for domains of attraction. Journal of Differential Equations. 2(2). 158–172. 9 indexed citations

12.

Loud, W. S.. (1965). Verzweigung periodischer Lösungen gewisser nichtlinearer Differentialgleichungen. ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik. 45(S1). 1 indexed citations

13.

Loud, W. S.. (1961). The Location of the Invariant Manifold for a Perturbed Autonomous System. Journal of Mathematics and Physics. 40(1-4). 87–102. 3 indexed citations

14.

Loud, W. S.. (1959). Periodic solutions of x"+cx'+g(x)=εf(t). American Mathematical Society eBooks. 15 indexed citations

15.

Loud, W. S.. (1959). Periodic solutions of 𝑥”+𝑐𝑥’+𝑔(𝑥)=𝜖𝑓(𝑡). Memoirs of the American Mathematical Society. 0(31). 0–0. 30 indexed citations

16.

Loud, W. S.. (1957). Boundedness and convergence of solutions of x''+cx'+g(x)=e(t). Duke Mathematical Journal. 24(1). 40 indexed citations

17.

Loud, W. S.. (1955). On Periodic Solutions of Duffing'u Equation with Damping. Journal of Mathematics and Physics. 34(1-4). 173–178. 12 indexed citations

18.

Loud, W. S. & C. R. Wylie. (1952). Advanced Engineering Mathematics.. American Mathematical Monthly. 59(8). 559–559. 542 indexed citations breakdown →

19.

Loud, W. S.. (1951). Functions with prescribed Lipschitz condition. Proceedings of the American Mathematical Society. 2(3). 358–360. 1 indexed citations

20.

Loud, W. S.. (1951). A Simple Iterative Solution for Certain Simultaneous Quadratic Equations. American Mathematical Monthly. 58(9). 609–613. 1 indexed citations

Rankless uses publication and citation data sourced from OpenAlex, an open and comprehensive bibliographic database. While OpenAlex provides broad and valuable coverage of the global research landscape, it—like all bibliographic datasets—has inherent limitations. These include incomplete records, variations in author disambiguation, differences in journal indexing, and delays in data updates. As a result, some metrics and network relationships displayed in Rankless may not fully capture the entirety of a scholar's output or impact.

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