A HYBRID NUMERICAL TECHNIQUE FOR SOLVING THREE-DIMENSIONAL SECOND-ORDER PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS
In this paper, a hybrid approach is presented for the numerical solution of three-dimensional parabolic partial differential equations. This new approach is applicable to both linear and nonlinear parabolic problems including systems. This hybrid numerical technique is based on the Haar wavelet coll...
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| Veröffentlicht in: | Fractals (Singapore) 2023, Vol.31 (2) |
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| creator | ASIF, MUHAMMAD AMIN, ROHUL HAIDER, NADEEM KHAN, IMRAN AL-MDALLAL, QASEM M. SAID, SALEM BEN |
| description | In this paper, a hybrid approach is presented for the numerical solution of three-dimensional parabolic partial differential equations. This new approach is applicable to both linear and nonlinear parabolic problems including systems. This hybrid numerical technique is based on the Haar wavelet collocation technique and the finite difference method. In this technique, the space derivative is approximated by truncated Haar wavelet series whereas the time derivative is approximated by finite difference method. The aforementioned proposed algorithms are very simple and can easily be implemented in any computer-oriented language efficiently. In order to demonstrate the efficiency and better accuracy of the newly developed numerical technique it is applied to some well-known examples from previous literature that comprises linear and nonlinear three-dimensional parabolic equations including systems. The obtained results affirm better accuracy and widespread applicability of the newly proposed numerical technique for a range of benchmark problems. |
| doi_str_mv | 10.1142/S0218348X23400182 |
| format | Article |
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This new approach is applicable to both linear and nonlinear parabolic problems including systems. This hybrid numerical technique is based on the Haar wavelet collocation technique and the finite difference method. In this technique, the space derivative is approximated by truncated Haar wavelet series whereas the time derivative is approximated by finite difference method. The aforementioned proposed algorithms are very simple and can easily be implemented in any computer-oriented language efficiently. In order to demonstrate the efficiency and better accuracy of the newly developed numerical technique it is applied to some well-known examples from previous literature that comprises linear and nonlinear three-dimensional parabolic equations including systems. The obtained results affirm better accuracy and widespread applicability of the newly proposed numerical technique for a range of benchmark problems.</description><identifier>ISSN: 0218-348X</identifier><identifier>EISSN: 1793-6543</identifier><identifier>DOI: 10.1142/S0218348X23400182</identifier><language>eng</language><publisher>Singapore: World Scientific Publishing Company</publisher><subject>Algorithms ; Approximation ; Finite difference method ; Hybrid systems ; Mathematical analysis ; Parabolic differential equations ; Partial differential equations</subject><ispartof>Fractals (Singapore), 2023, Vol.31 (2)</ispartof><rights>2023, The Author(s)</rights><rights>2023. The Author(s). This is an Open Access article in the “Special Issue on Applications of Wavelets and Fractals in Engineering Sciences”, edited by K. S. Nisar (Prince Sattam bin Abdulaziz University, Saudi Arabia), F. A. Shah (University of Kashmir, India), S. K. Upadhyay (Indian Institute of Technology, BHU, India), P. E. T. Jorgensen (University of Iowa, USA) published by World Scientific Publishing Company. 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This new approach is applicable to both linear and nonlinear parabolic problems including systems. This hybrid numerical technique is based on the Haar wavelet collocation technique and the finite difference method. In this technique, the space derivative is approximated by truncated Haar wavelet series whereas the time derivative is approximated by finite difference method. The aforementioned proposed algorithms are very simple and can easily be implemented in any computer-oriented language efficiently. In order to demonstrate the efficiency and better accuracy of the newly developed numerical technique it is applied to some well-known examples from previous literature that comprises linear and nonlinear three-dimensional parabolic equations including systems. The obtained results affirm better accuracy and widespread applicability of the newly proposed numerical technique for a range of benchmark problems.</description><subject>Algorithms</subject><subject>Approximation</subject><subject>Finite difference method</subject><subject>Hybrid systems</subject><subject>Mathematical analysis</subject><subject>Parabolic differential equations</subject><subject>Partial differential equations</subject><issn>0218-348X</issn><issn>1793-6543</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>ADCHV</sourceid><recordid>eNplkM1Og0AUhSdGE2v1AdyRuEbnDxiWFIYyCQU7gNEVKcOQ0NRSwcb49oI1brq69-ac757kAHCP4CNCFD9lECNGKHvFhEKIGL4AM-S4xLQtSi7BbJLNSb8GN8OwhRBSiugMHDwjeltIERhJseJS-F5s5NyPErEuuBGm0sjS-EUkSyOPJOdmIFY8yUSajL6M-2kSmKkMuDSePekt0lj405aLUQ5EGHLJk9-DrwsvH7HsFlw1m92g7_7mHBQhz_3IjNPllG4qYjnYdEhNXeYi23Ixqi2XWjXRuNFUEaVUbVXKYo6tGXIa5Tis1o3GFR0NqK7qqoJkDh5Ofw9993HUw2e57Y79fowsMUMEQdtGkwudXKrvhqHXTXno2_dN_10iWE7FlmfFjgw8MV9dv6sH1er9Z9u06h89R34A1XNxcA</recordid><startdate>2023</startdate><enddate>2023</enddate><creator>ASIF, MUHAMMAD</creator><creator>AMIN, ROHUL</creator><creator>HAIDER, NADEEM</creator><creator>KHAN, IMRAN</creator><creator>AL-MDALLAL, QASEM M.</creator><creator>SAID, SALEM BEN</creator><general>World Scientific Publishing Company</general><general>World Scientific Publishing Co. 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| language | eng |
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| source | World Scientific Open |
| subjects | Algorithms Approximation Finite difference method Hybrid systems Mathematical analysis Parabolic differential equations Partial differential equations |
| title | A HYBRID NUMERICAL TECHNIQUE FOR SOLVING THREE-DIMENSIONAL SECOND-ORDER PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS |
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