Introductory remarks

1971 ◽  
Vol 323 (1553) ◽  
pp. 153-153
Keyword(s):  
Social Sciences ◽  
Numerical Analysis ◽  
Numerical Methods ◽  
Future Development ◽  
Applied Mathematics ◽  
Numerical Techniques ◽  
Nonlinear Algebra ◽  
The Social ◽  
Linear And Nonlinear ◽  
Good Order

Over the last decade the use of numerical techniques for the solution of the problems of physics, engineering, chemistry, biology and the social sciences has increased by leaps and bounds, and it was felt that the time was ripe for holding a Discussion Meeting on some topic in numerical analysis. This was intended not merely to provide an opportunity for experts in the field to get together, since there are many specialized meetings in numerical analysis these days. The aim was rather to give scientists in general who are interested in numerical methods a chance to find out what is being done, so that they can make greater use of this work and hopefully influence its future development. After some deliberation I decided on partial differential equations as the topic, in spite of the fact that it is not an area in which I have made any direct contribution in recent years. This is because I believe it to be one of the most important and challenging fields; indeed the solution of systems of p. d. es lies at the very heart of the problems of applied mathematics. Long after we have the more basic fields of linear and nonlinear algebra and approximation theory in good order the problems arising in the solution of p. d. es will still be with us. The work that has been done in numerical analysis may then appear as a preliminary sharpening up of the tools we are to use.

scholarly journals Numerical Methods for Solving Fredholm Integral Equations of Second Kind

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
S. Saha Ray ◽  
P. K. Sahu
Keyword(s):  
Integral Equation ◽  
Numerical Methods ◽  
Integral Equations ◽  
Applied Mathematics ◽  
Fredholm Integral Equations ◽  
Nonlinear Fredholm Integral Equations ◽  
Linear And Nonlinear ◽  
Interdisciplinary Effort

Integral equation has been one of the essential tools for various areas of applied mathematics. In this paper, we review different numerical methods for solving both linear and nonlinear Fredholm integral equations of second kind. The goal is to categorize the selected methods and assess their accuracy and efficiency. We discuss challenges faced by researchers in this field, and we emphasize the importance of interdisciplinary effort for advancing the study on numerical methods for solving integral equations.

scholarly journals Numerical Methods for Advection Problem

2020 ◽  
Vol 13 (1) ◽  
pp. 144-157
Author(s):  
Diogene Vianney Pongui Ngoma ◽  
Germain Nguimbi ◽  
Vital Delmas Mabonzo ◽  
Narcisse Batangouna
Keyword(s):  
Mathematical Modeling ◽  
Numerical Analysis ◽  
Numerical Methods ◽  
Truncation Error ◽  
Numerical Techniques ◽  
Analytical Stability

This work is part of mathematical modeling and numerical analysis. This paper aims is to solve an advection problem where u=u(x; t) is the solution by Lax-Wendrof and nite dierence methods, to study the analytical stability in L2[0;1], L1[0; 1], then calculate the truncation error of these methods and nally study the analytical convergence of these methods. These numerical techniques of resolution were implemented in Scilab.

Early Numerical Analysis in Kepler's New Astronomy

2010 ◽  
Vol 23 (1) ◽  
pp. 39-63
Author(s):  
Steinar Thorvaldsen
Keyword(s):  
Numerical Analysis ◽  
Numerical Methods ◽  
Future Development ◽  
Transcendental Equation ◽  
Computational Power ◽  
Huge Amount ◽  
Johannes Kepler ◽  
The Future ◽  
Novel Methods ◽  
Improved Methods

ArgumentJohannes Kepler published hisAstronomia novain 1609, based upon a huge amount of computations. The aim of this paper is to show that Kepler's new astronomy was grounded on methods from numerical analysis. In his research he applied and improved methods that required iterative calculations, and he developed precompiled mathematical tables to solve the problems, including a transcendental equation. Kepler was aware of the shortcomings of his novel methods, and called for a new Apollonius to offer a formal mathematical deduction. He was also in great need of computational power, and his friend and colleague, Wilhelm Schickard, constructed the first prototype of a true mechanical calculator, although it never came into regular use. The article concludes that Kepler's new astronomy was clearly backed up by numerical methods and embedded concepts and challenges of great importance for the future development of numerical analysis.

scholarly journals China Studies in Germany

2016 ◽  
Vol 7 (1) ◽  
pp. 155-165
Author(s):  
Li Xuetao
Keyword(s):  
Social Sciences ◽  
United States ◽  
Future Development ◽  
The United States ◽  
Modern China ◽  
Chinese History ◽  
Research Methodologies ◽  
The Social ◽  
China Studies ◽  
The 1960S

Abstract China studies in Germany has undergone great changes since the 1960s. Influenced by burgeoning area studies in the United States, German scholarship shifted from traditional philological studies focused on translating and interpreting Chinese classics to practical studies of modern Chinese politics, economy, law, etc. Hence, there was also a shift in research methodologies to those of the social sciences. However, this shift, significant as it is, can never replace traditional Sinological studies aimed at Chinese history and classics. This paper uses Chinese history as an example to explore the development of German academic Sinology. It points out that research in traditional Sinology, as well as in modern China studies, no longer focuses on a particular discipline, but rather follows the trend toward interdisciplinary, comprehensive research. Hence we can expect that China studies will become increasingly decentralized and interactive in the future development of the field.

scholarly journals Numerical Methods for Advection Problem

2020 ◽  
Vol 13 (1) ◽  
pp. 144-157
Author(s):  
Diogene Vianney Pongui Ngoma ◽  
Germain Nguimbi ◽  
Vital Delmas Mabonzo ◽  
Narcisse Batangouna
Keyword(s):  
Mathematical Modeling ◽  
Numerical Analysis ◽  
Numerical Methods ◽  
Truncation Error ◽  
Numerical Techniques ◽  
Analytical Stability

This work is part of mathematical modeling and numerical analysis. This paper aims is to solve an advection problem where u=u(x; t) is the solution by Lax-Wendrof and nite dierence methods, to study the analytical stability in L2[0;1], L1[0; 1], then calculate the truncation error of these methods and nally study the analytical convergence of these methods. These numerical techniques of resolution were implemented in Scilab.

Overview of Numerical Methods for Predicting Flow-Induced Vibration

1988 ◽  
Vol 110 (1) ◽  
pp. 6-14 ◽  
Author(s):  
F. Axisa ◽  
J. Antunes ◽  
B. Villard
Keyword(s):  
Numerical Methods ◽  
Random Vibration ◽  
Fretting Wear ◽  
Predictive Analysis ◽  
Numerical Techniques ◽  
Flow Induced Vibration ◽  
Heat Exchanger Design ◽  
Flow Turbulence ◽  
Linear And Nonlinear ◽  
Key Aspects

A predictive analysis of an heat-exchanger design against severe vibration and wear has to cope with experimental data on flow-induced vibration and fretting wear, together with the use of analytical and numerical methods for predicting linear and nonlinear tube response. This paper describes a general approach of the problem currently under development at C.E.A. Attention is especially paid to some key aspects of the numerical techniques, namely, the modelization of flow-induced forcing functions and the modelization of impact and sliding at tube-support gaps. These topics are exemplified by numerical results related to some typical situations including the case of random vibration induced by flow turbulence and fluidelastic vibration.

The Uses of Statistics in the Social Sciences

1933 ◽  
Vol 26 (4) ◽  
pp. 210-221
Author(s):  
W. L. Crum
Keyword(s):  
Social Sciences ◽  
Statistical Theory ◽  
Social Science ◽  
Applied Mathematics ◽  
Mathematical Science ◽  
Thought Processes ◽  
The Social ◽  
Quantitative Basis ◽  
The Mind ◽  
Factual Data

Statistics and statistical methods have become so common a tool of the scientist, both for conducting his research and reporting his findings, that the ordinary layman is in danger of forgetting that statistical theory is a branch of mathematical science and that statistical practice is one type of applied mathematics. This important point should be constantly in the mind of everyone who uses statistics, whether as a producer or as a consumer. Nowhere is the danger of ignoring or forgetting this injunction greater than in the various fields of social science. Whether this is due to the great abundance of factual data and their ostensible bearing upon problems of timely interest, to the supposed necessity of putting reasoning in these fields on a quantitative basis at any cost, to the absence of traditional dominance by mathematical thought processes in these fields, or to other reasons, it is idle to speculate. The essential fact is that statistical workers in social science need particularly to be reminded that the vigorous and growing structure of statistical theory takes its root in mathematics.

scholarly journals Foreword to the special issue of EJAM on crime modelling

2010 ◽  
Vol 21 (4-5) ◽  
pp. 271-274 ◽  
Author(s):  
H. BERESTYCKI ◽  
S. D. JOHNSON ◽  
R. OCKENDON ◽  
M. PRIMICERIO
Keyword(s):  
Social Sciences ◽  
Social Science ◽  
Complex Systems ◽  
Applied Mathematics ◽  
Life Sciences ◽  
Special Issue ◽  
The Social ◽  
Long Time ◽  
Shed Light

This special issue is one of the very first dedicated to crime modelling in a journal of applied mathematics. It emphasizes one of the new areas at the Social Science frontier, where modelling and mathematical tools are put to use with a view to shed light on phenomena previously thought to be outside of their reach. Pioneering research is increasingly being carried out in many different areas in the life sciences or social sciences, often under the heading of the study of complex systems. When addressing issues regarding society, individuals or the collective behaviours of humans, several questions naturally arise about the modelling enterprise. What is the nature and role of modelling in social sciences? What is one to expect from these new approaches? The case of economics, which has relied on mathematics for a very long time now, can serve as a paradigm for what is happening in other social sciences.

What Can We Learn From Factorial Surveys About Human Behavior?

Methodology ◽  
2019 ◽  
Vol 15 (1) ◽  
pp. 19-30 ◽  
Author(s):  
Knut Petzold ◽  
Tobias Wolbring
Keyword(s):  
Social Sciences ◽  
Behavioral Intentions ◽  
Actual Behavior ◽  
Full Time ◽  
Factorial Survey ◽  
Survey Experiment ◽  
Intended Behavior ◽  
The Social ◽  
Survey Experiments ◽  
High Level

Abstract. Factorial survey experiments are increasingly used in the social sciences to investigate behavioral intentions. The measurement of self-reported behavioral intentions with factorial survey experiments frequently assumes that the determinants of intended behavior affect actual behavior in a similar way. We critically investigate this fundamental assumption using the misdirected email technique. Student participants of a survey were randomly assigned to a field experiment or a survey experiment. The email informs the recipient about the reception of a scholarship with varying stakes (full-time vs. book) and recipient’s names (German vs. Arabic). In the survey experiment, respondents saw an image of the same email. This validation design ensured a high level of correspondence between units, settings, and treatments across both studies. Results reveal that while the frequencies of self-reported intentions and actual behavior deviate, treatments show similar relative effects. Hence, although further research on this topic is needed, this study suggests that determinants of behavior might be inferred from behavioral intentions measured with survey experiments.

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