Numerical Methods for Partial Differential Equations

Top Research Topics at Numerical Methods for Partial Differential Equations?

The main points discussed in the journal deals with Mathematical analysis, Partial derivative, Finite element method, Applied mathematics and Nonlinear system. The study on Mathematical analysis presented in Numerical Methods for Partial Differential Equations intersects with the topics under Mixed finite element method. The journal explores topics in Mixed finite element method which can be helpful for research in disciplines like Extended finite element method and Finite volume method.

The studies on Partial derivative discussed can also contribute to research in the domains of Convergence (routing), Norm (mathematics), Finite difference and Stability (probability). The studies in Finite difference featured incorporate elements of Finite difference method and Finite difference coefficient. In the Finite element method research discussed, Discontinuous Galerkin method, Galerkin method and Superconvergence are all tackled.

While work presented in it provided substantial information on Applied mathematics, it also covered topics in Order (group theory), Mathematical optimization, Scheme (mathematics) and Calculus. Mixed boundary condition is a focus of the Boundary value problem works in it. Partial differential equation study tackled is connected to the field of Differential equation.

• Mathematical analysis (66.18%)
• Partial derivative (28.54%)
• Finite element method (25.63%)

What are the most cited papers published in the journal?

• Variational formulation for the stationary fractional advection dispersion equation (580 citations)
• Simple nonconforming quadrilateral Stokes element (503 citations)
• H‐p clouds—an h‐p meshless method (487 citations)

Research areas of the most cited articles at Numerical Methods for Partial Differential Equations:

The journal papers tackle a plethora of topics, such as Mathematical analysis, Partial derivative, Finite element method, Applied mathematics and Mixed finite element method. Many of the studies tackled in the journal articles connect Mathematical analysis with a similar field of study like Nonlinear system. The featured Partial derivative studies in the journal articles mainly concentrate on Boundary value problem but also cover areas of interest in Boundary (topology).

What topics the last edition of the journal is best known for?

• Mathematical analysis
• Quantum mechanics
• Partial differential equation

The previous edition focused in particular on these issues:

The journal mainly deals with areas of study such as Applied mathematics, Mathematical analysis, Finite element method, Order (group theory) and Nonlinear system. The concepts on Applied mathematics presented in it can also apply to other research fields, including Scheme (mathematics), Convergence (routing), Partial differential equation, Collocation method and Variable (mathematics). Discussions in Numerical Methods for Partial Differential Equations are anchored in the subject of Convergence (routing) and the similar topic of Stability (probability).

The presentations discussing Mathematical analysis offer insights in topics such as Boundary value problem, Finite difference method, Fractional diffusion, Finite difference and Space (mathematics). The Order (group theory) study featured in Numerical Methods for Partial Differential Equations draws parallels with the field of Fractional calculus.

The most cited articles from the last journal are:

• New numerical simulation for fractional Benney–Lin equation arising in falling film problems using two novel techniques (58 citations)
• A wavelet based numerical scheme for fractional order SEIR epidemic of measles by using Genocchi polynomials (38 citations)
• The reducing rank method to solve third‐order Duffing equation with the homotopy perturbation (34 citations)

Papers citation over time

A key indicator for each journal is its effectiveness in reaching other researchers with the papers published at that venue.

The chart below presents the interquartile range (first quartile 25%, median 50% and third quartile 75%) of the number of citations of articles over time.

Top authors and change over time

The top authors publishing in Numerical Methods for Partial Differential Equations (based on the number of publications) are:

• Mehdi Dehghan (49 papers) published 5 papers at the last edition,
• Hong Wang (30 papers) published 1 paper at the last edition,
• Zhi-zhong Sun (25 papers) published 1 paper at the last edition, 1 less than at the previous edition,
• Ismael Herrera (20 papers) absent at the last edition,
• Yinnian He (19 papers) published 1 paper at the last edition.

The overall trend for top authors publishing in this journal is outlined below. The chart shows the number of publications at each edition of the journal for top authors.

Top affiliations and change over time

Only papers with recognized affiliations are considered

The top affiliations publishing in Numerical Methods for Partial Differential Equations (based on the number of publications) are:

• Xi'an Jiaotong University (61 papers) published 4 papers at the last edition, 3 more than at the previous edition,
• Shandong University (56 papers) published 1 paper at the last edition, 1 less than at the previous edition,
• Amirkabir University of Technology (50 papers) published 5 papers at the last edition, 4 more than at the previous edition,
• National Autonomous University of Mexico (36 papers) absent at the last edition,
• University of South Carolina (34 papers) published 2 papers at the last edition.

The overall trend for top affiliations publishing in this journal is outlined below. The chart shows the number of publications at each edition of the journal for top affiliations.

Publication chance based on affiliation

The publication chance index shows the ratio of articles published by the best research institutions in the journal edition to all articles published within that journal. The best research institutions were selected based on the largest number of articles published during all editions of the journal.

The chart below presents the percentage ratio of articles from top institutions (based on their ranking of total papers).Top affiliations were grouped by their rank into the following tiers: top 1-10, top 11-20, top 21-50, and top 51+. Only articles with a recognized affiliation are considered.

During the most recent 2021 edition, 2.30% of publications had an unrecognized affiliation. Out of the publications with recognized affiliations, 7.08% were posted by at least one author from the top 10 institutions publishing in the journal. Another 6.60% included authors affiliated with research institutions from the top 11-20 affiliations. Institutions from the 21-50 range included 17.45% of all publications and 68.87% were from other institutions.

Returning Authors Index

A very common phenomenon observed among researchers publishing scientific articles is the intentional selection of journals they have already attended in the past. In particular, it is worth analyzing the case when the authors participate in the same journal from year to year.

The Returning Authors Index presented below illustrates the ratio of authors who participated in both a given as well as the previous edition of the journal in relation to all participants in a given year.

Returning Institution Index

The graph below shows the Returning Institution Index, illustrating the ratio of institutions that participated in both a given and the previous edition of the conference in relation to all affiliations present in a given year.

The experience to innovation index

Our experience to innovation index was created to show a cross-section of the experience level of authors publishing in a journal. The index includes the authors publishing at the last edition of a journal, grouped by total number of publications throughout their academic career (P) and the total number of citations of these publications ever received (C).

The group intervals were selected empirically to best show the diversity of the authors' experiences, their labels were selected as a convenience, not as judgment. The authors were divided into the following groups:

• Novice - P < 5 or C < 25 (the number of publications less than 5 or the number of citations less than 25),
• Competent - P < 10 or C < 100 (the number of publications less than 10 or the number of citations less than 100),
• Experienced - P < 25 or C < 625 (the number of publications less than 25 or the number of citations less than 625),
• Master - P < 50 or C < 2500 (the number of publications less than 50 or the number of citations less than 2500),
• Star - P ≥ 50 and C ≥ 2500 (both the number of publications greater than 50 and the number of citations greater than 2500).

The chart below illustrates experience levels of first authors in cases of publications with multiple authors.