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We have designed a cubic spline wavelet decomposition for the Sobolev space HO(2)(I) where I is a bounded interval. Based on a special 'point-wise orthogonality' of the wavelet basis functions, a fast Discrete Wavelet Transform (DWT) is constructed. This DWT transform will map discrete samples of a function to its wavelet expansion coefficients in O(N log N) operations. Using this transform, we propose a collocation method for the initial value boundary problem of nonlinear PDE's. Then, we test the efficiency of the DWT transform and apply the collocation method to solve linear and nonlinear PDE's. Wavelet

The Du Fort-Frankel difference scheme is generalized to difference operators of arbitrary high order accuracy in space and to arbitrary order of the parabolic differential operator. Spectral methods can also be used to approximate the spatial part of the differential operator. The scheme is explicit, and it is unconditionally stable for the initial value problem. Stable boundary conditions are given for two different fourth order accurate space approximations.

The Du Fort-Frankel difference scheme is generalized to difference operators of arbitrary high order accuracy in space and to arbitrary order of the parabolic differential operator. Spectral methods can also be used to approximate the spatial part of the differential operator. The scheme is explicit, and it is unconditionally stable for the initial value problem. Stable boundary conditions are given for two different fourth order accurate space approximations.

We have designed a cubic spline wavelet decomposition for the Sobolev space H(sup 2)(sub 0)(I) where I is a bounded interval. Based on a special 'point-wise orthogonality' of the wavelet basis functions, a fast Discrete Wavelet Transform (DWT) is constructed. This DWT transform will map discrete samples of a function to its wavelet expansion coefficients in O(N log N) operations. Using this transform, we propose a collocation method for the initial value boundary problem of nonlinear PDE's. Then, we test the efficiency of the DWT transform and apply the collocation method to solve linear and nonlinear PDE's.

The primary focus of this project was on the analysis and development of new parallel algorithms for the solution of linear and nonlinear initial/boundary value problems (IBVPs) in two space variables. Parabolic, second order hyperbolic, biharmonic, and Schrodinger type problems were considered. The new algorithms, which are alternating direction implicit (ADI) orthogonal spline collocation (OSC) methods employing C1 piecewise polynomial spaces of arbitrary order, have been implemented and their efficacy was demonstrated on test problems taken from the literature. Rigorous stability and convergence analyses of the methods were also carried out.

The primary focus of this project was on the analysis and development of new parallel algorithms for the solution of linear and nonlinear initial/boundary value problems (IBVPs) in two space variables. Parabolic, second order hyperbolic, biharmonic, and Schrodinger type problems were considered. The new algorithms, which are alternating direction implicit (ADI) orthogonal spline collocation (OSC) methods employing C1 piecewise polynomial spaces of arbitrary order, have been implemented and their efficacy was demonstrated on test problems taken from the literature. Rigorous stability and convergence analyses of the methods were also carried out.

Book Source: Digital Library of India Item 2015.225044 dc.contributor.author: Ratna Bhattacharya dc.date.accessioned: 2015-07-10T15:28:18Z dc.date.available: 2015-07-10T15:28:18Z dc.date.digitalpublicationdate: 2005-09-08 dc.identifier.barcode: 5990010120132 dc.identifier.origpath: /rawdataupload/upload/0120/134 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/225044 dc.description.scannerno: 15 dc.description.scanningcentre: IIIT, Allahabad dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 354 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher: Indian Institute Of Technology Kanpur dc.rights: Out_of_copyright dc.source.library: Indian Institute Of Technology Kanpur dc.subject.classification: Technology dc.subject.classification: Engineering. Technology In General dc.subject.classification: Mechanical Engineering In General. Nuclear Technology. Electrical Engineering. Machinery dc.title: Optimal Multistep Methods For Second Order Initial And Boundary Value Problems

Die Rahmenhandlung der Novelle "Der Heilige" bildet Hans der Armbruster, der im Jahre 1180 im Rückblick die dramatische Lebensgeschichte des Thomas Becket (1118-1170) erzählt. Dieser war von 1155 an Kanzler des englischen Königs Heinrich II (1133 - 1189). Die Novelle von Meyer gibt die historischen Tatsachen ziemlich genau wieder, mit Ausnahme der Gestalt von Grace, die eine Erfindung des Dichters ist. Thomas wurde bereits 1173 heilig gesprochen. (Zusammenfassung von Hans Hafen)

2Schuß von der Kanzel

By Conrad Ferdinand Meyer

Der Schuß von der Kanzel ist eine humoristische Novelle von Conrad Ferdinand Meyer (1825–1898), die vom Werk Gottfried Kellers beeinflusst ist und zwischen Mai und August 1877 entstanden ist. Sie wurde erstmals im Zürcher Taschenbuch auf das Jahr 1878 veröffentlicht.

Jürg Jenatsch ist der Titel eines 1876 erschienenen historischen Romans von Conrad Ferdinand Meyer über den Bündner Pfarrer und Militärführer Georg Jenatsch. Der Roman spielt in der Zeit des Dreißigjährigen Krieges. Zu Beginn des Krieges streben die Spanier danach, Graubünden unter ihre Gewalt zu bringen um damit die strategisch wichtigen Bergpässe unter Kontrolle zu bekommen. Den Spaniern tritt der junge protestantische Pastor Jürg Jenatsch entgegen. Er ist Anführer der protestantischen Bündnern, die angetreten sind, ihre Heimat zu verteidigen. Sein Gegenspieler auf der katholischen Seite ist der Freiherr Pompejus Planta. Provisorische Zusammenfassung von Wikipedia

We can never allow the great objective facts of Christianity, and their attendant doctrines, to sink low on our horizon; but we must give equal prominence to the demands of Christ for a righteousness which shall exceed that of the Scribes and Pharisees, and a perfection which shall resemble that of God. We have no right to be content with saying "Lord, Lord;" we must do the things which He says. <br /><br />Of course, the right kind of obedience is impossible, apart from the Cross and the Spirit. We must be reconciled before we can become obedient children; we must be filled with the Spirit before "the fragrance of Christ" can be manifested through us in every place. The Sermon on the Mount must be read in the transfiguring light which shines backwards from the later events in our Lord's life. <br /><br />When, however, this is borne in mind, each sentence of that marvelous discourse glistens with celestial radiance, and rings with the music of the Gospel. In such a spirit let us address ourselves to the study of the "Directory of the Devout Life," as it is contained in Matt. v., vi., and vii. (from the Preface)<br /><br />F. B. Meyer was a Baptist preacher and a friend and contemporary of D. L. Moody.

I remember seeing the huge Matterhorn reflected, in its minutest details, in a small mountain lakelet, many miles distant; and similarly, the life of Jesus is remarkably mirrored in this touching story. In fact, there are scenes in the life of Joseph which probably foreshadow events that are timed to happen in the near future, and which depict them with a vividness and minuteness not to be found elsewhere on the page of Scripture. It is here only that we can fully realize what will take place when the Lord Jesus makes Himself known to his brethren according to the flesh, and they exclaim, "It is Jesus our brother!" (From the Preface)

Kein geringerer als Dante Alighieri wird hier zum Erzähler. Am Fürstenhof in Verona gibt er seine Geschichte über den Mönch Astorre zum Besten, der, um seinem sterbenden Vater den letzten Willen zu gewähren, sein Mönchsgelübde bricht und heiratet, obwohl er dazu im Inneren keineswegs bereit ist. Er glaubt, einen richtigen Entschluss gefasst zu haben, als er sich mit Diana, der Witwe seines Bruders, verlobt. Doch das für ihn völlig neue weltliche Leben stellt ihn vor Bewährungsproben... - Summary by Eva K.

An old-world story this! In its strange Eastern dress, it appears to be as remote from us as the garb of an Arab, or the barter of an Oriental Bazaar. And yet human life is much the same, whenever and wherever lived. Our critics complain of our poring over these timeworn pages of ancient biography, but, with all deference to them, we feel bound to say that we learn better how to live, we inhale more spiritual ozone, we see further into the reasons of God's dealings with men, when doing so, than when scanning the pages of yesterday's newspaper, or of a society journal. Thousands of miles cannot part us from our kin across the seas; and thousands of years cannot part us from our kin across the ages, or sever the readers of these words from the son of Isaac, who, nearly drowned in the seas of his own craft and cunning, at length emerged a new man, and a prince with God. (Adapted by MaryAnn from Chapter 1)

"It has always seemed to me, amid submerged masses, deep down at the bottom of the ocean of human life, there are yearnings and desires for a better life, that ring sadly and perpetually. It has been the aim of my life to listen for these, and where I have detected them, to present the only answer -- the love of God in Jesus Christ our Lord.<br><br>Some of the ways in which I have sought to do this during my Leicester life are narrated in this book, which serves to show what may be done in this direction amid the cares of a busy pastorate." (from the Preface)

Rev. F. B. Meyer, a contemporary of D. L. Moody, offers a series of reflections on the 23rd Psalm. (Summary by MaryAnn)