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Use of Functional Approximation Methods in the Computer Solution of Initial Value Partial Differential Equation Problems
June 1969 (vol. 18 no. 6)
pp. 499512
ASCII Text  x  
R. Vichnevetsky, "Use of Functional Approximation Methods in the Computer Solution of Initial Value Partial Differential Equation Problems," IEEE Transactions on Computers, vol. 18, no. 6, pp. 499512, June, 1969.  
BibTex  x  
@article{ 10.1109/TC.1969.222702, author = {R. Vichnevetsky}, title = {Use of Functional Approximation Methods in the Computer Solution of Initial Value Partial Differential Equation Problems}, journal ={IEEE Transactions on Computers}, volume = {18}, number = {6}, issn = {00189340}, year = {1969}, pages = {499512}, doi = {http://doi.ieeecomputersociety.org/10.1109/TC.1969.222702}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  Use of Functional Approximation Methods in the Computer Solution of Initial Value Partial Differential Equation Problems IS  6 SN  00189340 SP499 EP512 EPD  499512 A1  R. Vichnevetsky, PY  1969 KW  Analog computers KW  computer integration KW  functional approximations KW  Hermitian problems KW  hybrid computers KW  initial value problems KW  integral transform methods KW  numerical solution KW  partial differential equations KW  Ritz?Galerkin method KW  Sturm?Liouville transform methods. VL  18 JA  IEEE Transactions on Computers ER   
Methods of functional approximation for the computer solution of initial value partial differential equation problems provide a device by which these solutions can be approximated by those of initial value problems in sets of ordinary differential equations. A number of ways to achieve this have been suggested, some of them general, some of them utilizing specific properties of the equations at hand. What all these methods have in common is the fact that the solution u(x, t) of a partial differential equation in space x and time t is approximated by a function u*(a1(t), a2(t), . . ., aN(t)), where the dependence upon x is prescribed. In most applications, u* is linear in the ai(t), i.e., u*= =ai(t)fi(x). The ai(t) satisfy a set of ordinary differential equations obtained as the result of the approximation process. This system of ordinary differential equations is then integrated by classical analog or digital computer methods.
Index Terms:
Analog computers, computer integration, functional approximations, Hermitian problems, hybrid computers, initial value problems, integral transform methods, numerical solution, partial differential equations, Ritz?Galerkin method, Sturm?Liouville transform methods.
Citation:
R. Vichnevetsky, "Use of Functional Approximation Methods in the Computer Solution of Initial Value Partial Differential Equation Problems," IEEE Transactions on Computers, vol. 18, no. 6, pp. 499512, June 1969, doi:10.1109/TC.1969.222702
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