The improved complex variable element-free Galerkin method for two-dimensional Schrödinger equation
A numerical study of two-dimensional Schrödinger equation is carried out using the improved complex variable element-free Galerkin (ICVEFG) method. The ICVEFG method involves employment of the improved complex variable moving least-squares (ICVMLS) in the element-free Galerkin (EFG) procedure for nu...
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| Veröffentlicht in: | Computers & mathematics with applications (1987) 2014-11, Vol.68 (10), p.1093-1106 |
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| container_title | Computers & mathematics with applications (1987) |
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| creator | Zhang, L.W. Deng, Y.J. Liew, K.M. Cheng, Y.M. |
| description | A numerical study of two-dimensional Schrödinger equation is carried out using the improved complex variable element-free Galerkin (ICVEFG) method. The ICVEFG method involves employment of the improved complex variable moving least-squares (ICVMLS) in the element-free Galerkin (EFG) procedure for numerical approximation. The ICVMLS is used to construct trial functions for the two-dimensional Schrödinger equation in the form of one-dimensional basis function that effectively reduces the number of unknown coefficients. In this study, the applicability of the ICVEFG method is examined through a number of numerical example problems. Convergence studies are carried out for these example problems by varying the number of nodes to ascertain convergent results are achieved as the number of nodes increases. The stability and accuracy of the ICVEFG method are validated by comparing the computed results with the exact solutions. |
| doi_str_mv | 10.1016/j.camwa.2014.07.024 |
| format | Article |
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The ICVEFG method involves employment of the improved complex variable moving least-squares (ICVMLS) in the element-free Galerkin (EFG) procedure for numerical approximation. The ICVMLS is used to construct trial functions for the two-dimensional Schrödinger equation in the form of one-dimensional basis function that effectively reduces the number of unknown coefficients. In this study, the applicability of the ICVEFG method is examined through a number of numerical example problems. Convergence studies are carried out for these example problems by varying the number of nodes to ascertain convergent results are achieved as the number of nodes increases. 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The ICVEFG method involves employment of the improved complex variable moving least-squares (ICVMLS) in the element-free Galerkin (EFG) procedure for numerical approximation. The ICVMLS is used to construct trial functions for the two-dimensional Schrödinger equation in the form of one-dimensional basis function that effectively reduces the number of unknown coefficients. In this study, the applicability of the ICVEFG method is examined through a number of numerical example problems. Convergence studies are carried out for these example problems by varying the number of nodes to ascertain convergent results are achieved as the number of nodes increases. The stability and accuracy of the ICVEFG method are validated by comparing the computed results with the exact solutions.</description><subject>Approximation</subject><subject>Complex variables</subject><subject>Convergence</subject><subject>Galerkin methods</subject><subject>Galerkin’s procedure</subject><subject>Improved complex variable element-free Galerkin method</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Schroedinger equation</subject><subject>Two dimensional</subject><subject>Unsteady Schrödinger equation</subject><issn>0898-1221</issn><issn>1873-7668</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNp9kLlOxDAURS0EEsPyBTQuaRKe7SxOQYEQmzQSBVBbXl4YD0k82JkBfowf4McIDDXVk57uudI9hJwwyBmw6myZW92_6ZwDK3Koc-DFDpkxWYusriq5S2YgG5kxztk-OUhpCQCF4DAj7nGB1PerGDboqA39qsN3utHRa9MhxQ57HMasjYj0RncYX_xAexwXwdE2RDq-hcz5KZN8GHRHH-wifn06PzxjpPi61uP0PyJ7re4SHv_dQ_J0ffV4eZvN72_uLi_mmRWSjZlpyqLVEoxDbmUNTpaNYdKWXJpSuwaNLksDbWN4LYRrDdjaFcI2VlpuRSkOyem2d5rzusY0qt4ni12nBwzrpFhVAZQFr5spKrZRG0NKEVu1ir7X8UMxUD9O1VL9OlU_ThXUanI6UedbCqcVG49RJetxsOh8RDsqF_y__DeEZYPg</recordid><startdate>201411</startdate><enddate>201411</enddate><creator>Zhang, L.W.</creator><creator>Deng, Y.J.</creator><creator>Liew, K.M.</creator><creator>Cheng, Y.M.</creator><general>Elsevier Ltd</general><scope>6I.</scope><scope>AAFTH</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>201411</creationdate><title>The improved complex variable element-free Galerkin method for two-dimensional Schrödinger equation</title><author>Zhang, L.W. ; Deng, Y.J. ; Liew, K.M. ; Cheng, Y.M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c381t-b954fa80bde2c870d859b18c528b5ad9eba55b0f9b2733dfb0c7d43c9c8c2c353</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Approximation</topic><topic>Complex variables</topic><topic>Convergence</topic><topic>Galerkin methods</topic><topic>Galerkin’s procedure</topic><topic>Improved complex variable element-free Galerkin method</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Schroedinger equation</topic><topic>Two dimensional</topic><topic>Unsteady Schrödinger equation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Zhang, L.W.</creatorcontrib><creatorcontrib>Deng, Y.J.</creatorcontrib><creatorcontrib>Liew, K.M.</creatorcontrib><creatorcontrib>Cheng, Y.M.</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Computers & mathematics with applications (1987)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Zhang, L.W.</au><au>Deng, Y.J.</au><au>Liew, K.M.</au><au>Cheng, Y.M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The improved complex variable element-free Galerkin method for two-dimensional Schrödinger equation</atitle><jtitle>Computers & mathematics with applications (1987)</jtitle><date>2014-11</date><risdate>2014</risdate><volume>68</volume><issue>10</issue><spage>1093</spage><epage>1106</epage><pages>1093-1106</pages><issn>0898-1221</issn><eissn>1873-7668</eissn><abstract>A numerical study of two-dimensional Schrödinger equation is carried out using the improved complex variable element-free Galerkin (ICVEFG) method. The ICVEFG method involves employment of the improved complex variable moving least-squares (ICVMLS) in the element-free Galerkin (EFG) procedure for numerical approximation. The ICVMLS is used to construct trial functions for the two-dimensional Schrödinger equation in the form of one-dimensional basis function that effectively reduces the number of unknown coefficients. In this study, the applicability of the ICVEFG method is examined through a number of numerical example problems. Convergence studies are carried out for these example problems by varying the number of nodes to ascertain convergent results are achieved as the number of nodes increases. The stability and accuracy of the ICVEFG method are validated by comparing the computed results with the exact solutions.</abstract><pub>Elsevier Ltd</pub><doi>10.1016/j.camwa.2014.07.024</doi><tpages>14</tpages><oa>free_for_read</oa></addata></record> |
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| language | eng |
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| source | Elsevier ScienceDirect Journals Complete; EZB-FREE-00999 freely available EZB journals |
| subjects | Approximation Complex variables Convergence Galerkin methods Galerkin’s procedure Improved complex variable element-free Galerkin method Mathematical analysis Mathematical models Schroedinger equation Two dimensional Unsteady Schrödinger equation |
| title | The improved complex variable element-free Galerkin method for two-dimensional Schrödinger equation |
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